title: Kitty Pryde

text: Shadowcat's popularity had a profound effect on the real-life Kitty Pryde: the latter became so overwhelmed by attention from Shadowcat fans, she abbreviated her name to K.D. Pryde to avoid association with her fictional counterpart. She has since stated she has mixed feelings about her fame, saying she values Byrne's comics for their entertainment and artistic value, but wishes more people would appreciate her as more than just Shadowcat's namesake.


title: Kitty Pryde

text: Katherine Anne "Kitty" Pryde was born in Deerfield, Illinois, to Carmen and Theresa Pryde. She is an Ashkenazi Jewish-American and her paternal grandfather, Samuel Prydeman, was held in a Nazi concentration camp during World War II. Kitty started to have headaches at age thirteen, signaling the emergence of her mutant powers. She was approached by both the X-Men's Charles Xavier and the Hellfire Club's White Queen, Emma Frost, both of whom hoped to recruit her for their respective causes. Kitty was unnerved by Frost, observing that the White Queen looked at her as if she were "something good to eat." She got along better with Xavier and the three X-Men who escorted him, quickly becoming friends with Ororo Munroe. Ororo told Kitty who she really was and about the X-Men, which made the teenager even more enthusiastic about attending Xavier's school.


title: Kitty Pryde

text: Their conversation was cut short when they (along with Wolverine and Colossus) were attacked by armored mercenaries in the employ of Frost and the Hellfire Club. The X-Men defeated their assailants, but were subdued by the White Queen's telepathic powers immediately after. In the confusion, Kitty was separated from the X-Men, and not captured along with them. She managed to contact Cyclops, Phoenix, and Nightcrawler. With the help of Dazzler and Pryde, those X-Men rescued their teammates from the Hellfire Club.


title: Kitty Pryde

text: The White Queen appeared to perish in the battle, which meant she was no longer competing with Xavier for the approval of Kitty's parents. Kitty's parents had not heard from her in more than a day, because during that time she was first being pursued by the Hellfire Club's men and then working with the X-Men to save their friends. All they knew was Kitty had left with Xavier's "students" to get a soda, there had been reports that the soda shop had been blown up, and Kitty had been missing since. Therefore, they were angry at Xavier when he finally returned with Kitty in tow. At first, it seemed like there was no chance of Kitty being allowed to attend the school and join the X-Men. Phoenix then used her considerable telepathic power to erase the memories of Kitty's parents and plant false ones, resulting in a complete shift in their attitude towards Xavier. Kitty was then allowed to enroll at Xavier's school with her parents' blessing, becoming the youngest member of the team.


title: Kitty Pryde

text: Kitty joined the X-Men, and assumed the costumed identity of Sprite. Early in her career as an X-Man, Kitty's adult self from an alternate future took possession of her body in the present to help X-Men thwart the assassination of Senator Robert Kelly by the second Brotherhood of Evil Mutants. Kitty then singlehandedly defeated a N'Garai demon. Kitty also briefly attended the White Queen's Massachusetts Academy when her parents became convinced that she needed to be with students of her own age, but following a failed attempt to subdue the X-Men, Frost revoked Kitty's admission.


title: Kitty Pryde

text: During her teen years, Kitty fostered a number of close relationships with others at the school and in the X-Men. She developed a crush on Colossus and became close friends with his little sister Illyana Rasputin. Initially uneasy around Nightcrawler and other mutants with physical deformities, Kitty finally overcame her fears and became close friends with him. Kitty also befriended Lockheed, a highly intelligent alien resembling a dragon, who followed her home after a mission in outer space. Lockheed is extremely loyal to Kitty, and the two of them share a psychic bond. Wolverine became something of a mentor to Kitty despite his usually gruff personality. Storm came to view Kitty as the daughter she never had.


title: Kitty Pryde

text: Though Xavier has threatened to reassign Kitty to the New Mutants, a team of younger mutants he established in the absence of the X-Men, ever since the X-Men returned from outer space, she never ended up joining the group, who she derisively calls the "X-Babies". Kitty was later abducted by the Morlocks and nearly forced to wed Caliban. She was then abducted by the White Queen, but rescued by the New Mutants.


title: Kitty Pryde

text: During this time, Kitty began to date Colossus, although this did not last long. Colossus developed feelings for an alien woman named Zsaji whom he met on the Beyonder's planet in the first Secret Wars. Colossus' feelings toward Zsaji were primarily a side effect of her own unique healing abilities, which she had used on him after he became injured. Regardless, Colossus' feelings were real and he returned to Earth consumed with grief after Zsaji's death. He admitted to Kitty that he loved Zsaji, which hurt her deeply and ended the budding romantic relationship. Kitty had made good friends with a local boy from Salem Central named Doug Ramsey around this time, but her feelings for him never went as deep as his for her, and they never actually dated, though they remained close, even more so after Doug's status as a mutant was revealed and he joined the New Mutants under the codename Cypher. They remained friends until his death some time later.


title: Kitty Pryde

text: During the 1984–1985 "Kitty Pryde and Wolverine" miniseries, Kitty is possessed by a demon, the ninja Ogun. Ogun psychically bestows upon Kitty a virtual lifetime of martial arts training. Kitty was brainwashed by Ogun into becoming a ninja assassin, and was sent to attack Wolverine. Kitty is able to resist Ogun's influence with Wolverine's help, and the two form a strong teacher/student bond, which helps them in vanquishing Ogun. Kitty returns to the X-Men, no longer the innocent girl they once knew, and officially adopts the codename Shadowcat.


title: Kitty Pryde

text: While trying to save Rogue, Kitty was badly injured by Harpoon's energy spear during the Mutant Massacre story arc, in the massacre of the Morlocks, with the result that she lost control of her power and was stuck in an intangible state and could not regain her solidity. She was rushed to Muir Island along with other surviving casualties of the Massacre to be tended to by Moira MacTaggert. MacTaggert was able to keep Kitty's condition from deteriorating to the point where she completely lost physical substance and ceased to exist, but was not able to do any more to help her.


title: Kitty Pryde

text: At this time, Kitty's natural state was to be intangible. Where she once had to make a conscious effort to phase, she could now only maintain her solidity through an act of conscious will. The X-Men went to Reed Richards, Mister Fantastic of the Fantastic Four, for aid, but Richards initially refused because he was not sure he would be able to help.


title: Kitty Pryde

text: Having nowhere else to go, the X-Men turned to Richards' enemy Doctor Doom. This created a moral dilemma for both the X-Men and the Fantastic Four, and both teams fought each other because the Fantastic Four were trying to stop the treatment while the X-Men were determined to save Kitty's life. In the end, both the personal crisis of the Fantastic Four and the life of Shadowcat were saved after Franklin Richards, with the help of Lockheed, brought both teams to their senses. Kitty has since recovered from this state and now has full control over her power again.


title: Kitty Pryde

text: Among the others injured and brought to Muir Isle were Colossus and Nightcrawler, although Colossus left the United Kingdom shortly after being released from MacTaggert's care to join the rest of the X-Men on their mission to battle the Adversary. The X-Men sacrificed their lives to defeat the Adversary, the battle and their sacrifice was televised and broadcast across the world. The X-Men were resurrected later in the same issue, unknown to the world at large, but chose to keep a low profile and perpetuate the belief that they were still dead. This strategy was enforced to more effectively fight their enemies. This meant avoiding contact with friends and family, including Kitty. Thinking the X-Men were dead, Kitty and Nightcrawler joined Rachel Summers, Captain Britain, and Meggan to form the Britain-based team Excalibur following an adventure in which they saved Rachel from Technet. For a brief time, Kitty studied at St. Searle's School for Girls in Britain. During her time with Excalibur, Kitty developed a crush on Professor Alistaire Stuart which went unreciprocated since Alistaire was attracted to Rachel. Later, she was romantically involved with former Black Air agent Pete Wisdom. At some point Kitty was recruited by the international law enforcement agency S.H.I.E.L.D. to repair the computer system of their flying headquarters. Kitty discovered the problem was due to Ogun's spirit having infiltrated the computer system, and with the aid of Wolverine, she managed to purge Ogun's presence. During this time, Kitty was attracted to a S.H.I.E.L.D. intern her own age, and this made her begin to doubt her relationship with Wisdom. Soon after, she broke off their relationship.


title: Kitty Pryde

text: After Excalibur's dissolution, Shadowcat, Nightcrawler, and Colossus return to the X-Men. While returning, they faced a group of imposters following Cerebro, in the guise of Professor X. While tracking Mystique, she stumbles onto prophetic diaries that belonged to Irene Adler, a precognitive. During the six-month gap, Kitty visited Genosha. Whatever she experienced there is unknown (although presumably connected to her father, living on Genosha at the time), but it had a profound effect on her. She cut her hair and began to act rebelliously, also using one of Wolverine's bone claws broken off during battle as a weapon. Kitty remained with the X-Men for a while before leaving after the apparent death of Colossus. Trying to give herself a normal life, she attended the University of Chicago. During this time, her father was killed when Cassandra Nova’s Sentinels destroyed Genosha. Kitty later finds a recording of his death due to exploring footage of the attack. She is also kidnapped by William Stryker, but the X-Treme X-Men team helped her escape, and she assisted them on several missions.


title: Kitty Pryde

text: At the start of Joss Whedon's run on "Astonishing X-Men", Kitty once again rejoins the X-Men, despite having extreme reservations about working with the former White Queen, given their history. This was the primary reason why Frost herself wanted Kitty on the team, as a sort of "safety" should Frost ever revert to type. Frost reasoned that the person who trusted her least would be most likely to spot such behavior. On one of the team's first missions, Shadowcat discovered Colossus was alive. After some initial awkwardness, Kitty and Colossus resumed dating.


title: Kitty Pryde

text: Kitty Pryde appeared alongside Colossus in the "Blinded by the Light" arc in X-Men. They are the two X-Men left to look after the students while the rest of the X-Men leave for Mystique's home in Mississippi to check up on Rogue, during which they are ambushed by the Marauders. Kitty and Colossus, meanwhile, attempt to protect the students from a faction of the Marauders led by Exodus. It is revealed over the course of the story that Kitty, worried of the Destiny Diaries' safety, devised a plan with Cyclops and Emma Frost to hide them and have Emma wipe the location from her mind. The location could only be revealed by a code word spoken to Kitty. The arc concludes with a battle between Iceman and Cannonball against the Marauders for the diaries, during which they are destroyed by Gambit.


title: Kitty Pryde

text: In the "Torn" arc, the latest incarnation of the Hellfire Club begin an assault on Xavier's School. Kitty fulfilled the role that Emma Frost envisioned, personally taking down Frost and imprisoning her, only to fall under a telepathic delusion created by Hellfire member Perfection, who claimed to be the true, unreformed Emma Frost. Under this delusion, Kitty was made to believe that she and Colossus had conceived a child, which was later taken away by the X-Men because its potential mutant abilities were supposedly dangerous. Kitty reacts in the delusion by attempting to rescue the child from a near-inescapable "box" in the depths of the school, unaware that in reality she is freeing an alien entity, Stuff, who contains the trapped consciousness of Cassandra Nova, the apparent ringleader of this new Hellfire Club. A newly awakened Cyclops revealed that the new Hellfire Club, including Perfection and Nova, are actually mental projections created by a piece of Cassandra Nova's consciousness; which became lodged in Emma's mind during the X-Men's last confrontation with her, playing on her survivor's guilt over the Genoshan massacre, and utilizing Emma's telepathy to both confound the X-Men and orchestrate her (Nova's) escape from the Stuff body. As Cyclops killed the mental projections, Emma tried to force Kitty to kill her to get rid of Nova. Undeterred, Cassandra Nova switched her focus to attempt to transfer her mind to Hisako Ichiki. It appears that Nova did not succeed, as the team was transported to S.W.O.R.D.'s air station en route to Ord's Breakworld for the "Unstoppable" arc that concludes Whedon's run on "Astonishing X-Men".


title: Kitty Pryde

text: As the team prepares to end the confrontation with the Breakworld leader, the team splits up—with Kitty on the team appointed to stop the missile pointed at Earth. Kitty phases into the missile to disrupt its circuitry noting that it is composed of the same material as the rest of Breakworld, a material that is difficult and exhausting for her to phase through. After phasing for a mile into the missile, Kitty finds the center only to discover it empty. The missile is fired, causing Kitty to pass out inside of it as Beast discovers too late that due to its shape, trajectory, and lack of internal circuitry, the Breakworld's weapon is not a missile, but a bullet. As the bullet hurtles toward Earth, Kitty lies unconscious within it.


title: Kitty Pryde

text: As the situation becomes increasingly dire, Emma establishes mental contact with Kitty, reassuring her that she will come out of this fine, though it eventually becomes clear to both that the situation will be grim. Kitty and Emma come to an understanding and reconciliation, Emma stating that she never wanted something like this to happen to her. Kitty then phases the bullet through Earth, but is trapped within. At the end of "Giant-Size Astonishing X-Men", Scott Summers mentions that Doctor Strange, Reed Richards, and some "top men" tried to save her, but believe she has fused to the bullet, as it continues to hurtle through space. Whether she is alive or dead is unknown, though the X-Men consider her lost to them.


title: Kitty Pryde

text: As a result of these events Kitty does not appear in the X-Men crossover event , since this takes place after the events of "Giant-Size Astonishing X-Men". She is briefly mentioned in the aftermath of the Messiah Complex, by Colossus, Nightcrawler, and Wolverine, as the three of them discuss "losing her."


title: Kitty Pryde

text: To cope with Kitty's loss, Colossus takes down a group of Russian criminals dealing in human trafficking, and gets a tattoo of the name 'Katya' on his chest. Emma begins having a recurring dream in which she hears a voice whom she believes is Kitty's trying to reach out to her.


title: Kitty Pryde

text: It was later confirmed by Abigail Brand that Kitty Pryde was still alive within the bullet, but because the bullet's design would harden as time went on, it would become increasingly difficult to break the bullet open.


title: Kitty Pryde

text: After the X-Men move to the island of Utopia, Magneto arrives on the island professing his desire to join and support the X-Men in their effort to unite the world's remaining mutants. The X-Men reluctantly let him stay, remaining wary of him despite his efforts to gain their trust. In a final bid to gain their trust, Magneto focuses his powers, attempting to divert the interstellar path of the metal bullet Kitty is trapped in and bring her home to Earth. Meanwhile, inside the bullet, Kitty is revealed to still be alive. Unbeknownst to the others, Magneto had encountered the bullet earlier while attempting to regain his powers with the High Evolutionary and surmised that Kitty was inside. Despite this and the High Evolutionary's apparent ability to retrieve the bullet and Kitty, Magneto chose to focus on regaining his powers, secretly keeping tabs on the bullet until his decision to draw it back to Earth. During her time trapped inside the bullet, Kitty keeps herself and the bullet phased to avoid collisions with any inhabited objects in its path.


title: Kitty Pryde

text: Magneto brings Kitty Pryde safely down to Earth by cracking the bullet in two and levitating Kitty to the ground. When she and Colossus try to touch, it is revealed that she is trapped in her intangible form, unable to speak, and the X-Men place her in a protective chamber similar to the one used for her following the events of the Mutant Massacre. How Kitty survived her time in the bullet is unclear to the X-Men's science team, where the X-Men discover that all her bodily functions halted. An analysis by Kavita Rao hypothesizes that Kitty created an intense muscle memory to keep herself and the bullet phased and has "forgotten" how to un-phase.


title: Kitty Pryde

text: During a conversation with Colossus, with Emma Frost acting as the psi-conduit, Kitty picks up Emma's stray thoughts on killing the captive Sebastian Shaw, to prevent Namor from discovering she previously lied to him. While disgusted at Emma's intentions, Kitty offers a compromise. Due to her current ghost state, she is the perfect tool for making Shaw disappear.


title: Kitty Pryde

text: In a storyline in "Uncanny X-Men", the Breakworlders make their way to Earth. During the conflict between the Breakworlder Kr'uun and the X-Men, Kitty is slain and resurrected by Kr'uun's mate in an alien ritual, which results in her powers returning to normal.


title: Kitty Pryde

text: Shortly thereafter, Kitty breaks up with Colossus, and decides to return with Wolverine to Westchester to open the Jean Grey School for Higher Learning. In "Wolverine and the X-Men" #4, she appears to be suddenly pregnant, but the pregnancy was revealed to be a Brood infestation, and it was swiftly dealt with by a team of X-Men. Since returning to Westchester, Kitty has shared several kisses with Iceman. During the events of "Avengers vs. X-Men", Kitty does not take a side, but instead decides to stay at the school to work with the students. Once Bobby returned from working with the X-Men after realizing that the Phoenix had corrupted them, he and Kitty finally decide to go on a date.


title: Kitty Pryde

text: After Beast brings the original five X-Men into the future to stop Cyclops in the present, Kitty volunteers to take responsibility for the temporally relocated X-Men while they work to undo this dark future. This soon puts her at odds with the rest of her team as they believed the original five should go back to their own time in order to prevent any damage to the space-time continuity. Eventually, this leads Kitty to take the decision of abandoning the school with the time-displaced X-Men and join Cyclops's X-Men at the New Xavier School. During the first few weeks at the New Xavier School, Jean Grey is abducted by the Shiar Empire to stand trial for her future self's crimes. Kitty and the time-displaced X-Men team up with the Guardians of the Galaxy and succeed in rescuing Jean from the Shiar. At the conclusion of the storyline, Kitty begins a long-distance, flirtatious relationship with Starlord, Peter Quill.


title: Kitty Pryde

text: In the following weeks, Kitty's relationship with Peter Quill evolves more and more as they developed stronger feelings for each other every day. At one point, Quill gets captured during one of their dates and she has no option but to go to his rescue, despite her fear of space as a result of her being trapped on the giant space bullet. After rescuing Peter, she decides to stay in space with him. Then, Kitty convinces Peter to steal a powerful artifact called the Black Vortex from his father J'son. Soon, they find themselves being chased by J'son's assassination squad, the Slaughter Lords. In despair, they request the aid of the X-Men and the Guardians of the Galaxy to protect the Vortex. After a few of their own friends can't resist the temptation and submit to the Vortex, betray the team, and escape with the artifact; the team splits and Kitty stays in Spartax to help an orphanage. She is encased in amber after Thane (who was allied with J'son) freezes the whole planet along with the people inside it; but thanks to her phasing powers, she manages to get out of the amber. Then the Brood attacks Spartax, planning to use every encased person to lay eggs and create an army of Brood to start invading other planets and conquering them. Kitty feels the only way to stop them is by submitting to the Vortex herself as she's the only one who can resist the cosmic corruption. She reluctantly submits and becomes a being of unlimited power. After being reminded of the love between her and Peter Quill, she goes back and phases all the amber that encased Spartax, along with the Broods trying to infect the people, and sends them all to another dimension. Kitty doesn't give up the cosmic power but admits to Peter that she is afraid of it. Peter promises her that he will never abandon her no matter how much she changes. Then, Peter kneels and proposes marriage to Kitty. She, with tears in her eyes, accepts. Later when Star Lord is declared Emperor of Spartax she is told she will become the first lady of Spartax.


title: Kitty Pryde

text: Kitty takes on the mantle of Star Lord and joins the Guardians of the Galaxy in Peter Quill's place so he can take on his royal duties. When Hala the Accuser massacres Spartax in an attempt to make Quill pay for J'son's actions against her people, she initially easily lays waste to the capitol and overpowers the Guardians. After the Guardians regroup and formulate a strategy to defeat her, Kitty manages to partially phase Hala into the ground so the rest of the Guardians can knock her out and separate her from her weapon. After Quill loses his title as king he and Kitty end up on a mission with the rest of the Guardians on a concentration camp prison planet owned by the Badoon after Gamora gave them information on it so they can free Angela. Once there, Kitty has a personal reaction upon seeing the prisoners and makes it her mission to liberate everyone there and defeat the captors, as it reminds her of Nazi concentration camps. After Quill gets captured and sentenced to death in an arena battle, Kitty finds and kills one of the Badoon leaders by phasing his heart out of his body. When Captain Marvel summons the Guardians to Earth to help her address Tony Stark, Kitty learns that Thanos is a prisoner on Earth and tries to convince Quill to tell Gamora. When fighting starts Kitty woefully realizes that some of her former students are on Tony Stark's side instead of fighting with Captain Marvel. During the battle the Guardians' ship was destroyed, effectively stranding them on Earth. After helping the Guardians stop Thanos from leading an invasion from the Negative Zone the Guardians are given a new ship; however, Kitty decides to stay on Earth and ends her time with the Guardians and Quill.


title: Kitty Pryde

text: Upon returning to Earth, Kitty hopes to finally regain a semblance of a normal life but ends up approached by Storm, who informs Kitty of everything the X-Men have gone through while Kitty was away. Storm announces to Kitty that she intends to step down as leader of the X-Men due to the guilt that she feels for leading the X-Men to war and offers Kitty her position. After touring X-Haven and seeing how much things have changed and how much things need to change for the better, Kitty agrees to lead the X-Men as long as Storm remains on the team. Her next act is to relocate the mansion from Limbo to Central Park, New York so the X-Men can refocus on being part of the world instead of fearing it under the belief that if the X-Men truly are to be seen as heroes, then they need to actually live in the world that they are trying to save instead of constantly worrying about their own survival.


title: Kitty Pryde

text: Under Kitty's new leadership, the X-Men go through some small changes in order to shed their history and make new names for themselves, such as convincing Rachel Summers to change her code name to Prestige and renaming the mansion as The Xavier Institute for Mutant Education and Outreach. Kitty learns first-hand how hard it is to balance leading the X-Men as well as managing the mansion when there are many political factors trying to deliberately get in the way of the X-Men. She also begins to have awkward one-on-one moments with Colossus; they try to remain friends, but given their long history their interactions swiftly become complicated. Kitty's first case as field leader of the X-Men sees her and her team taking on a new Brotherhood of Evil Mutants. After discovering that an outspoken anti-mutant politician brainwashed this new Brotherhood to work for her to publicly discredit mutants, Kitty threatened to expose her if she continued exploiting mutants for her own personal gain.


title: Kitty Pryde

text: After Krakoa became a new sovereign nation for Mutants, Kitty Pryde, now going by Captain Kate Pryde, discovers she is the sole mutant who is, for unknown reasons, unable to use the various warp gates leading to Krakoa. It is implied that she has done something to anger Krakoa, but that restriction does not mean Kitty cannot use other means to reach the mutant homeland. She steals a boat and sets sail for the island. Kitty's time on Krakoa proves to be just as fruitless, as the island's natural resources (like flowers that grow into biome homes) are similarly prohibited to Kitty. Emma Frost comes asking Kitty to take up a special mission: taking a bigger boat out to serve as pirate captain on the X-Men's mission to liberate mutants trapped in oppressive countries that do not recognize mutant sovereignty, while also smuggling and supplying for Emma's Hellfire Trading Company the lifesaving drugs the X-Men provide to humans. Kate Pryde is later appointed the new Red Queen of the Hellfire Trading Company by Emma Frost, to the dismay of Sebastian Shaw. Seeing Pryde as an obstacle to his complete control of the Hellfire Corporation, Shaw began plotting against Kate and her crew. After taking notice how Emma became overprotective of the newly crowned Red Queen, Shaw realized that for the same reason she can't travel through Krakoa's gates nor read or understand the Krakoan language until Emma implanted it in her brain, the X-Men's Resurrection Protocols also won't apply to her, which means Kate cannot be resurrected if she died. He orchestrated a distraction by paying off human supremacists Homines Verendi to stage an attack on his own son. Once Kate was defenseless, Shaw emerged from below deck and ensnared Lockheed with a net gun, making him a helpless hostage. He then released Krakoan seeds at her feet, which wrapped around her and prevented her from using her powers. He then dropped her and Lockheed into the sea. While Lockheed was able to survive, Kate sank helplessly, and once her head dropped under the surface, she had no air left and drowned instantly. Her death is later confirmed by Bishop as he retrieves Kate's body, as it was also established that the Resurrection Protocols indeed do not apply to Kate, as the Five, for reasons unknown, cannot resurrect her. However, she is later resurrected, as Emma Frost realized that it was due to the nature of Kate's intangibility powers that her mindless body was unable to break out of the egg.


title: Kitty Pryde

text: Kitty is a mutant with the ability to pass through solid matter by passing her atomic particles through the spaces between the atoms of the object through which she is moving. In this way she and the object through which she is passing can temporarily merge without interacting, and each is unharmed when Shadowcat has finished passing through the object. This process is called "phasing" or quantum tunneling and it renders her almost completely intangible to physical touch. Shadowcat passes through objects at the same speed at which she is moving before she enters them. Since she is unable to breathe while inside an object, she can only continuously phase through solid objects (as when she travels underground) as long as she can hold her breath. However, contrary depictions of the duration of her phasing ability have been presented, such as when she has phased miles within an object. The use of her abilities also interferes with any electrical systems as she passes through by disrupting the flow of electrons from atom to atom, including the bio-electric systems of living bodies if she concentrates in the right way. This typically causes machines to malfunction or be destroyed as she phases through them, and can induce shock and unconsciousness in living beings.


title: Kitty Pryde

text: Using her power began as an optional ability, but for a period (over ten years of published comics, approximately two years in-continuity) Kitty existed in a naturally "phased" state, and had to consciously choose to become solid. Kitty has returned to her original form and is normally solid and must choose to use her power. While phasing, she does not physically walk on surfaces, but rather interacts with the molecules of air above them, allowing her to ascend and descend, causing her to seemingly walk on air. While phased, she is immune to most physical attacks, and has inconsistent showings of some resistance to telepathy. The density of some materials (such as adamantium) can prove deleterious to her phasing, causing her to be severely disoriented or experience pain if she tries to pass through them. Some energy attacks also prove problematic for Kitty. For example, an energy blast fired by Harpoon, a member of the Marauders, caused her to lose her ability to become fully tangible for months. Magic and magical beings can also harm her in her phased state, as demonstrated in a battle with a N'Garai demon whose claws left no visible marks, but caused Kitty severe pain as they passed through her intangible body.


title: Kitty Pryde

text: Kitty can also extend her powers to phase other people and objects. She is able to phase at least six other people (or objects of similar mass) with her, so long as they establish and maintain physical contact with her. She can extend her phasing effect to her own clothing or any other object with mass up to that of a small truck, as long as she remains in contact with it. Kitty can also make objects intangible by maintaining contact with them. She has threatened to leave people phased into a wall, and used her power offensively to harm the Technarch Magus, and Danger.


title: Kitty Pryde

text: Kitty's powers seem to have increased over the years. During an "X-Treme X-Men" story arc in which she is kidnapped by Reverend William Stryker, she phases out of sync with Earth's rotation to move from one place in the world (only east or west) to another seemingly instantaneously. At the climax of "Astonishing X-Men", Kitty phases a 10 mi (16 km) long "bullet" composed of super-dense alien metals through the entire planet Earth. This feat caused her considerable strain, but she is unable to phase out of the bullet. Moreover, originally Kitty found it difficult or impossible to phase only part of her body at a time. In the Days of Future Past story arc, she is possessed by her older future self, allowing her to solidify only her shoulder while phasing the rest of her body through Destiny—a feat explicitly beyond the 13-year-old Kitty's abilities. By contrast, the Kitty Pryde of Joss Whedon's run can punch and kick someone standing on the other side of a wall, selectively phasing and unphasing body parts as necessary. She can even run and leap through an armed opponent, grabbing their weapon as she passes by, which presumably requires her to solidify only the surface area of the palms of her hands and then immediately phase both her palms and the weapon.


title: Kitty Pryde

text: Besides her mutant powers, Kitty is a genius in the field of applied technology and computer science. She is highly talented in the design and use of computer hardware. She is a skilled pilot of piston and jet engine aircraft, and a competent pilot of certain advanced interstellar vehicles. She has previously shown a unique ability to wield the Soulsword and also be harmed by it. Since her possession by the ninja demon Ogun, she has been consistently shown to be an excellent hand-to-hand combatant, having since been endowed with a lifetime of training in the martial arts of Japanese ninja and samurai.


title: Kitty Pryde

text: She is a professional-level dancer in both ballet and modern dance. She speaks fluent English, Japanese, Russian, and the royal and standard languages of the alien Shi'ar and Skrull, and has moderate expertise in Gaelic, Hebrew, and German.


title: Kitty Pryde

text: Kitty also shares a mental/empathic connection with her pet dragon Lockheed; both she and the alien dragon can "sense" each other's presence at times and generally understand one another's thoughts and actions.


title: Kitty Pryde

text: When Kitty used the Black Vortex, her powers were augmented to a cosmic scale making her a god-like being. She can phase through any material of any density and can even phase a planet out of Thane's amber, whereas in her normal state it is an extremely difficult task to simply phase herself out of the amber. She can also apparently transverse between the planes of the multiverse and is immune to the effects of space. Her appearance can be changed but her natural form appears to be rather gaseous in look.


title: Kitty Pryde

text: Chris Arrant of "Newsarama" referred to Kitty Pryde as one of the "best Marvel characters of all time," writing, "The X-Men are amazing - uncanny, even - but it wasn't until Kitty Pryde entered the picture that readers gained a real perspective of how uncanny. Created as a 'girl next door'/grounded character in the original Chris Claremont/John Byrne era, Shadowcat was a hit character from the start - and she only got better over the years. [...] Of all the mutant characters, Kitty Pryde has proven to be the most human when it comes to evolution and growth, And that doesn't just make it stand out among her fellow X-Men, but among the entire Marvel Comics pantheon as well." David Uzumeri of "ComicsAlliance" described Kitty Pryde as a "fan-favorite phasing mutant," stating, "She had an appropriately temporary permanent goodbye, and then she was gone, careening through the void in a ballistic dong. When you think about it, this is somewhat appropriate for a character who's largely fulfilled the role of "dream girlfriend" for the majority of X-Men writers and readers. Because for a character who purportedly acts as a role model for girls and women, she's always seemed like more of a wish-fulfillment fantasy for nerdy teenagers (and fetishistic British comic writers). Kitty was always pretty close to perfect; whatever errors she made were always well-intentioned. [...] The fact is, Kitty's moral perfection has become her character, since everyone loves her so much that nobody wants to drag her through any mud. Because she almost never makes mistakes, she can't really progress as a character by learning from them – she's a patron saint." Eric Diaz of "Nerdist" called Kitty Pryde "smart and resourceful," saying, "The character of Kitty was introduced in 1980, in the middle of the legendary run from creators Chris Claremont and John Byrne on Uncanny X-Men. The 14 year old mutant, who could phase through solid objects, was the youngest member of the team and the wish fulfillment character for millions of kids who read X-Men comics. Fans got to see Kitty grow up to become a competent and capable leader over the years. For non-comics fans, she was maybe best known for being part of the X-Men arcade game from the early ’90s, which was based on the animated pilot Pryde of the X-Men.But Katherine Pryde, despite her popularity, has never had much in the way of solo stories to base a movie on." Kat Vendetti of "ComicsVerse" called Kitty Pryde a "protector and a hero," asserting, "Throughout her history, Kitty Pryde’s characterization has been both intricate and multifaceted. She has used her strength and wit to save the X-Men, but she also embraces her emotions to stand up for what she wants. She can save the day when others can’t, and she’s also not afraid to express her more vulnerable sides. Through it all, Kitty Pryde never shies away from representing everything she stands for. From the moment we met her and as we continue to know her, Kitty has proven time and again to be a natural and worthy leader. Kitty Pryde remains the best choice to lead the team in X-Men Gold; she has everything it takes to be the best leader the X-Men have ever had."


title: Kitty Pryde

text: Jonathan Thompson of "CBR.com" referred to Kitty Pryde as the "heart and soul of the X-Men," stating, "Ever since she first appeared in 1980’s "Uncanny X-Men" #129, Kitty Pryde has been a symbol of female empowerment for fans. She may have seemed like just another teenage mutant who can phase through solid matter, but she was not to be underestimated. [...] Yet, despite this long history in the comics, many people may not know Kitty as well as they think they do. How can she send someone’s consciousness back in time in "X-Men: Days of Future Past"? How powerful is she? Does she have a romantic past with Colossus in the films? Is that story about the origin of her name true? If you got your X-Men education from the films rather than the comics, there is a lot worth learning about Kitty that makes her a fuller character on the screen. Alternatively, if you have followed Kitty for years through the source material, you may have some questions (or critiques) regarding the live-action version. And then, of course, there is the world of animation which reinterpreted Kitty in a few different ways. No matter what your preferred medium is, there is undoubtedly something more to learn about her." Nick Abadzis of "Tor.com" wrote, "Kitty led a long line of mutant teenagers who, in turn, represent the disaffected and disenchanted, the rebellious and the geeky. But Kitty was the first and somehow remains the archetype. Her powers initially seemed a secondary element in the appeal of the character, whose intelligence and Jewish ancestry were highlighted. Yet Kitty’s ability to “phase” was, to a degree, an ingenious metaphor for that teenage desire to sometimes just disappear. Who, at that age, hasn’t sometimes felt dumb and socially awkward enough to want the world to just swallow them up? Kitty could do it—and it was so cool. [...] Outside the X-Men the reader, through Kitty, caught further glimpses of what it might be like to be a mutant—or, crucially, a member of any minority group—which, in turn, helped elevate the comic book from simple monthly melodrama into an ongoing saga and pop cultural phenomenon." Thomas Bacon of "Screen Rant" asserted, "Nobody could have predicted just how influential Kitty Pryde would be. In a recent Twitter thread, "The Claremont Run" noted Kitty became Claremont's favorite "viewpoint character," the lens through which readers experienced the X-Men. It was a smart move because Claremont was indulging in increasingly adult themes. Kitty made her debut in the middle of the "Dark Phoenix Saga" - and her youthful perspective heightened the narrative impact. But Claremont was quick to ensure readers that Kitty was a capable and competent new addition [...] Brian Bendis openly admits she was his comic book crush, which explains why Kitty wound up dating Peter Parker in his "Ultimate Spider-Man" relaunch. Warren Ellis infamously aged her up so she could have a relationship with the mutant Pete Wisdom, who was basically Ellis' own analog in the Marvel Comics Universe. But her greatest impact was through Joss Whedon, who recalled that famous issue of a teenager who was capable enough to take down a demon when he was creating "Buffy the Vampire Slayer". In fact, Whedon has gone so far as to refer to Kitty as the mother of Buffy, the main inspiration for the Slayer." Hilary Goldstein and Richard George of "IGN" stated, "Most mutants come to Xavier's having experienced great trauma and difficulty in their youth. Kitty arrived as an innocent with the seemingly innocuous power to turn intangible. She is the mutant everyman, the common girl turned superhero. Marvel has attempted to replicate Kitty Pryde on several occasions, most notably with Jubilee, but there's something special about Kitty that puts her above the rest. She's strong-willed, creative and fiercely loyal. Just as her pet dragon, Lockheed, became instantly attached to Kitty, we were hooked early on. Who could have guessed long ago that she would become one of the most endearing characters in the X-Men Universe?"


title: Kitty Pryde

text: According to Diamond Comic Distributors, "Star-Lord and Kitty Pryde" #1 was the 39th best selling comic book in July 2015.


title: Kitty Pryde

text: Brian Delpozo of "ComicsVerse" stated, ""Star-Lord and Kitty Pryde" #1 is one of the best issues to come out of Marvel’s “Secret Wars” storyline so far. While its plot is a bit exposition heavy at the start, it eventually starts moving at a brisk pace, with very strong characters and fun art. If the darkness of most of Battleworld is bringing you down, I’d definitely recommend giving this issue a read." Levi Hunt of "IGN" gave "Star-Lord and Kitty Pryde" #1 a grade of 8.8 out of 10, writing, ""Star-Lord and Kitty Pryde" is a Disney movie of a comic -- and that’s not just because Peter Quill spends half the issue singing Little Mermaid songs. Peter is one of the only survivors of the 616-Marvel Universe still alive and now he is hiding out among God Doom’s people, just trying not to get caught. Suddenly his life changes when he meets an alternate-reality version of his fiancé – Kitty Pryde. This book has all the hijinks, humor, and heart of Tangled or Aladdin, and that’s just where the Disney comparisons start. Alti Firmansyah draws this book with all of expressive, big-eyed, joy of Disney minimalism. It perfectly complements Sam Humphries’s wonderful story and makes for an enjoyable read for (almost) all ages."


title: Kitty Pryde

text: In addition to her mainstream incarnation, Kitty Pryde has been depicted in other fictional universes.


title: Kitty Pryde

text: In the Age of Apocalypse reality, Kitty grows up under harsh circumstances and her nature reflects it. She has short hair, tight clothes, and chain smokes cigarettes. Her parents are killed in the Chicago Cullings, and she is forcibly recruited into Apocalypse's army, but is later rescued by Colossus. Magneto puts Shadowcat under Weapon X's training, hoping to turn her into the X-Men's assassin, and she is given a set of retractable artificial claws around each wrist to better imitate her teacher's fighting style. After the fallout between Colossus and Magneto, Shadowcat sides with Colossus, whom she has married. Instead of leaving the fight against Apocalypse altogether, the couple become the teachers of Generation Next. The two submit their trainees to harsh situations, giving them little comfort despite the fact that Shadowcat is close to the age of her students.


title: Kitty Pryde

text: Shadowcat assists the team in rescuing Illyana Rasputin from the Seattle Core, and, at Colossus' behest, abandons her students after Illyana is saved. She is killed by Colossus in his ruthless obsession to protect his sister, Illyana; coming between an enraged Colossus and his endangered sister, Shadowcat never believed he would harm her.


title: Kitty Pryde

text: In the "Days of Future Past" timeline (Earth-811), Shadowcat goes by the name Kate Pryde. Kate attempts to go back in time to prevent the assassination of Senator Robert Kelly by Mystique and the Brotherhood of Evil Mutants. She succeeds, only to create a separate timeline where the events of her past still come to pass. After returning to her own time Kate helps Rachel Summers escape back to the timeline she just created. Captured by Sentinels, Kate escapes by phasing through her inhibitor collar and fell into a time warp, causing her to merge with the Sentinel that was scanning her, and arrives in the timeline Rachel is inhabiting. Kate's mind settles in a small, metal, off-spherical body and becomes known as Widget. After a few adventures in that timeline, mostly in company with her Earth-616 counterpart's team Excalibur, Kate regains her memory and returns to her original timeline where she is able to reprogram the ruling Sentinels to protect life, ending their tyranny.


title: Kitty Pryde

text: In "Earth X" it is revealed in the appendix of issue six that Kitty Pryde is killed saving Colossus while he could not shift into his metal form. Instead of phasing the bullet through her, she heroically takes the bullet and is killed.


title: Kitty Pryde

text: A version of Kitty Pryde codenamed Cat first appeared in "Exiles" #96. She is younger than her Earth-616 counterpart. She has the appearance and powers of the normal Shadowcat although she wears a different costume. Prior to her joining the Exiles, this version of Kitty had been recruited by Emma Frost as one of the core agents of the Hellfire Club's strike force. She helps Psylocke defeat Doom's soldiers who have invaded the Panoptichron. She helps retrieve Blink, Morph, and Sabretooth from being scattered across the multiverse. She works as a computer expert for the team and is a full member of the Exiles.


title: Kitty Pryde

text: Cat's skill with using her powers means she is not tied to any dimension and can see through various realities, including those of the mind (for instance seeing the various personalities in Sage's mind as "ghosts" surrounding her). Her arrival in the Crystal Palace and connection to its computers has increased this, giving her the ability to "cascade" through different alternative versions of herself, altering her appearance and details of her powers. Amongst other versions, she has assumed the form of a Kitty Pryde with the appearance and powers of Tigra. During the New Exiles' last mission Cat faced off against Madame Hydra (Sue Storm) and killed her at the cost of her own life.


title: Kitty Pryde

text: There has been another version of Kitty that appeared in the King Hyperion story arc ("Exiles" #38-40). She had survived an attack on the X-Mansion by the Sentinels. The Colossus from her universe had been killed in the attack but she had the same feelings towards Weapon X's Colossus even though he was not her Colossus. The two eventually fell in love with each other. Unfortunately this did not last since she died with Colossus when they were shot into the empty vacuum of space by Hyperion.


title: Kitty Pryde

text: When the Scarlet Witch altered reality in the 616 Universe, creating the reality known as House of M where mutants were the dominant population, Kitty Pryde was a teacher in a public middle school in Cincinnati, Ohio. Like many of the heroes of Earth 616, she is reminded of the true reality by Layla Miller and recruited in the fight to restore reality.


title: Kitty Pryde

text: In the limited series "Magik (Illyana and Storm)", an alternative reality Kitty renames herself "Cat" after she is mutated by the demonic sorcerer Belasco into a more feline form, with cat eyes, whiskers, a tail, and enhanced physical abilities and senses. Trapped in Belasco's Limbo, Cat takes a militant view towards defeating the sorcerer, eschewing the magic that her reality's Storm embraces, instead turning to skills in swordplay and physical combat. She tries to save the Illyana Rasputin of Earth-616 from corruption through magic by taking Illyana into the wilderness of Limbo and teaching the child to fight and survive. Like the Kitty Pryde of Earth-616 eventually would, Cat became Illyana's best friend, but more in the role of an older sister due to the difference in their ages.


title: Kitty Pryde

text: Cat's plan goes awry when the pair's attempt to confront Belasco fails, at the cost of the life of an enslaved Nightcrawler; Illyana falls under Belasco's influence and Cat is further transformed towards a feline, with a semi-animalistic mind completely loyal to Belasco. Cat is eventually slain by Illyana when Belasco sets Cat upon his rebellious apprentice; facing death at Cat's hands and knowing that, deep down, a part of Kitty still exists and hates her enslavement, Illyana broke Cat's neck in self-defense.


title: Kitty Pryde

text: Long after Illyana overthrows Belasco, escapes Limbo, and becomes a member of the junior X-Men team known as the New Mutants, Cat's remains are found by the team in Limbo's throne room. By then she had completely decomposed to a skeleton. Illyana, facing a rebellion of Limbo's demon population that threatened to overrun Earth, smashed Cat's skull in rage over the demonic taint that Belasco left on her soul and frustration over the horrible choice she had to make to kill Cat.


title: Kitty Pryde

text: Kitty is briefly shown in the background as a zombie in "Ultimate Fantastic Four" #23, despite her mutant phasing powers. She is also seen in "Marvel Zombies: Dead Days", when zombie Alpha Flight attack the X-Men. This would appear to have been retconned, though, as of "Marvel Zombies: Halloween," which depicts her and her son Peter with Colossus surviving for several years in an out of the way house farm, encountering zombies, but, fortunately, being rescued by Mephisto, who dispatched the remaining zombies.


title: Kitty Pryde

text: The Earth-91126/Earth-Z Kitty is recruited by Earth-2149/Marvel Zombies Spider-Man to help him develop a cure for the zombie hunger, on the grounds that her powers mean that she would be in no danger from him if he should succumb to his zombie instincts, but she is later seemingly killed when the zombie Quasar holds her underwater until she is forced to become solid once more, allowing the infected Namor to eat her flesh (much to the rage of the zombie Wolverine, of Earth-2149).


title: Kitty Pryde

text: Storm was taken by the vampire Dracula and unlike Earth 616, she does not return. Kitty goes off to battle her, either to save or kill her. Kitty slays several vampires in the way but Storm proves too much for her and Kitty becomes her unwilling slave for some time. She later shows up as the Black Queen of the Hellfire Club and seems to be none too happy with Storm. It's also hinted that she was engaged or going to be engaged to Colossus. Her ultimate fate at the end of the series is unknown.


title: Kitty Pryde

text: In the reality of Earth-597, an alternative universe where World War II was won by Nazi Germany, Kitty is forced to serve as Shadowcat alongside Nightcrawler, Meggan, and Hauptmann Englande as a member of the Lightning Force (a version of Excalibur), made a virtual slave because of her Jewish heritage. She leads a sad existence and is easily identified by her shaved head and the Star of David tattooed on her forehead. It is indicated, from her own statements and those made by her reality's counterpart of Moira MacTaggert, that this Shadowcat is a true ghost, raised from the dead by a combination of science and magic and bound to serve the Nazi regime. This Shadowcat had the added ability to disrupt life force with her phasing power, knocking her victims unconscious, much like how her counterpart in the "prime" Marvel Universe (Earth-616) can disrupt technology that she phases through. She is also able to alter her facial features to a "demonic" aspect when attacking enemies or else responding to aggressive, commanding behavior from her superiors.


title: Kitty Pryde

text: Kitty tells Illyana a bedtime story and casts herself as Pirate Kitty Pryde, captain of the "Abdul Alhazred", who operated in a magical world. Unlike her mainstream counterpart, she did not have any mutant powers and wore a classic pirate outfit which also included her Star of David necklace. She was also sometimes known as Colleen. Kitty was good friends of her version of Colossus, the Bamfs (Nightcrawler), Windrider (Storm), the "Fiend-with-no-name" (later revealed to be named "Mean") (Wolverine) and Lockheed (an alternative version of the X-Jet). Kitty also helped her versions of Professor X and Cyclops capture and cure that universe's version of Dark Phoenix.


title: Kitty Pryde

text: At first she was only a fairy tale character, but later it is revealed that her fairy tale is actually an alternative universe. (In fact, several members of this universe, the Bamfs, would later come to Earth-616 to cause trouble.) When Earth-616's Nightcrawler was temporarily stranded in her world, Kitty helped him defeat the sorcerer Shagreen and also encountered the Earth-616 versions of Illyana, Lockheed, and herself.


title: Kitty Pryde

text: In the native universe of the Exiles member Nocturne, Kitty is a senior member of the X-Men led by Nightcrawler. She is a teacher and TJ refers to her as "Aunt Kate". During a fight with Apocalypse Kitty gets exposed to a machine that reverts her to a younger stage of her life when she had only been with the X-Men a few weeks. Nocturne helps Kitty fit into the school and becomes her best friend. She also proves useful in the fight against the Brotherhood led by Cyclops.


title: Kitty Pryde

text: Imprisoned alongside other mutants at a prison camp in Texas by President X, Kitty attempted to use her phasing powers to escape, only to get stuck halfway through her cell door, losing three feet of intestines in the process.


title: Kitty Pryde

text: During the "Secret Wars" storyline, a version of Kitty named Kitten resides in the "wuxia"-inspired K'un-L'un region of Battleworld. In this reality, Kitten is a martial artist who joins Callisto's band of outcasts after being expelled from her school for attempting a forbidden technique, a side effect of which left her intangible. Kitten and her fellow outcasts became pupils of Shang-Chi, the exiled son of Emperor Zheng Zu. Dubbing their new school "The Lowest Caste", Shang-Chi represents the group as their master for the tournament deciding the next Emperor of K'un-L'un, hoping to usurp his father's tyrannical rule. Kitten accompanies Shang-Chi for each of his fights in the Thirteen Chambers. During his final fight with Zu, Shang-Chi uses Kitten's technique of intangibility, which leads to his eventual victory and replaces his father as the new Emperor of K'un-L'un.


title: Kitty Pryde

text: The Ultimate version of Shadowcat (Kitty Pryde) first appears as a 14-year-old girl in "Ultimate X-Men" #21. She is also Jewish and wears the Star of David around her neck, but does not appear to possess the same genius IQ as her mainstream (Earth-616) counterpart.


title: Kitty Pryde

text: Kitty's mother, worried about Kitty's mutation, seeks help from Professor Charles Xavier. Kitty becomes a student at Xavier's school, when her mother allows her to attend under the condition she does not take part in any X-Men missions, nor train in any "Danger Room" simulations. Kitty soon rebels against this and joins the X-Men as their youngest member. She idolizes Spider-Man and has a crush on him; she even dates Peter Parker for a time. After a fierce argument with Professor Xavier concerning Peter's secret identity, which his Aunt May had just found out about, Kitty leaves the X-Men and enrolls in Peter's school. Their relationship is strained after their romantic involvement (as superheroes) becomes publicly known, making it impossible for them to date anymore in their civilian identities, and eventually comes to an end when Peter realizes he cannot get over his feelings for Mary Jane. However, Kitty still retains strong feelings for him.


title: Kitty Pryde

text: Following the disastrous flood triggered by Magneto and the subsequent ban of public use of mutant powers, Kitty assumes the identity of the Shroud. Kitty also discovers that she can also decrease the space between her atoms make herself super-dense, giving her both superhuman strength and durability. When the authorities see Kitty as a threat, she enters into a fierce rage and demonstrates these powers for the first time to her friends. She is strong and angry enough to punch Spider-Man several feet through the air. She eventually escapes and goes into hiding in the now abandoned Morlock Tunnel with Iceman and the Human Torch after Peter Parker's death.


title: Kitty Pryde

text: Kitty makes an appearance in "", locating Jimmy Hudson, who is revealed to be Wolverine's son. Kitty was charged by Logan before his death to locate Jimmy and reveal his true origins to him.


title: Kitty Pryde

text: After the death of Spider-Man she formed new team of X-Men consisting of herself, Iceman and the Human Torch. They soon rescued the mutant Rogue from the mutant-hunting Nimrod robots, going on to recruit Jimmy Hudson into their group as well. After killing the mutant-hunting William Stryker, Kitty decided to leave New York for the Southwest along with Bobby, Rogue, and Jimmy (leaving only Johnny behind) in order to save the mutants there and defeat the Nimrods, now controlled by the deceased Stryker's consciousness.


title: Kitty Pryde

text: In the reality where Gwen Stacy is Spider-Woman, Kitty is an agent of S.H.I.E.L.D.'s Black Ops department, where she works closely with Wolverine to keep him in check and to help him fight his immortal curse. Like the Age of Apocalypse version, she also wields artificial claws on her wrists. It's revealed that she works with Logan out of guilt, as Stryker forced her to use her powers to subject Logan to the Weapon X experiment.


title: Kitty Pryde

text: An X-Baby version of Shadowcat appears briefly in the X-Babies one-shot comic. She is wearing her original costume and is younger than the other X-Babies. She is named as Shadowkitty rather than Shadowcat or Kitty Pryde. She also doesn't seem to have a strong bond with the X-Baby version of Lockheed.


title: Kitty Pryde

text: In the "X-Men Forever" series, Kitty and Nightcrawler have left Excalibur and rejoined the X-Men after the events of X-Men #1-3. Of the X-Men, she undergoes the most drastic changes from the events of "X-Men Forever" #1. During the battle with Fabian Cortez, she phases through Wolverine while he is being affected by Cortez's power. This drives her powers haywire as well, and somehow she ends up with one of Wolverine's claws in her wrist. Claremont has also hinted in dialogue throughout the title so far that she may have also undergone psychological or psychic changes as a result of the event. From "Forever" #4 to the current issue, she is shown to be able to use the claw in the exact method Wolverine would manifest it, with no apparent ill effects (the mechanism for this has not yet been made clear) outside of excruciating pain. Because of the merger with Logan's DNA she has begun to develop a healing factor, slower than Wolverine's but it heals faster when she is intangible. She has also slightly enhanced senses, she also can produce a set of five retractable claws on her left hand like Sabretooth. She has also begun to take on Logan's personality and memories as well. And because of this she is beginning to wonder what part of her truly remains the same.


title: Kitty Pryde

text: In the "" original English language manga one-shot graphic novel from Marvel and DelRay, Kitty is the newest and only female student of the all-male Xavier School for Gifted Youngsters, which is now experimenting with having a co-ed student body. As the sole girl, she becomes the center of attention and attraction for the rest of the students. She becomes a member and the mascot of the elitist fraternity, The Hellfire Club, and has a short-lived romantic relationship with the school troublemaker Pyro.


title: Kitty Pryde

text: In the "" future, Kitty Pryde becomes the mayor of Chicago and then President of the United States. She has three children: her eldest daughter, named Meredith, and twins 10 years younger than Meredith, Sara and Doug, with an unnamed partner who died protecting her from an assassination attempt.


title: Bass guitar

text: The bass guitar, electric bass or simply bass (), is the lowest-pitched member of the string family. It is a plucked string instrument similar in appearance and construction to an electric or an acoustic guitar, but with a longer neck and scale length, and typically four to six strings or courses. Since the mid-1950s, the bass guitar has largely replaced the double bass in popular music.


title: Bass guitar

text: The four-string bass is usually tuned the same as the double bass, which corresponds to pitches one octave lower than the four lowest-pitched strings of a guitar (typically E, A, D, and G). It is played primarily with the fingers or thumb, or with a pick. To be heard at normal performance volumes, electric basses require external amplification.


title: Bass guitar

text: According to the "New Grove Dictionary of Music and Musicians", an "Electric bass guitar [is] a Guitar, usually with four heavy strings tuned E'–A'–D–G." It also defines "bass" as "Bass (iv). A contraction of Double bass or Electric bass guitar." According to some authors the proper term is "electric bass". Common names for the instrument are "bass guitar", "electric bass guitar", and "electric bass" and some authors claim that they are historically accurate.


title: Bass guitar

text: The scale of the bass is located along the length of the string (from the nut to the bridge) and forms what is known as the fingerboard. The scale can range in length but is traditionally 34-35 inches long while "short scale" bass guitars are usually between 30 and 32 inches.


title: Bass guitar

text: Bass pickups are generally attached to the body of the guitar and located beneath the strings. They are responsible for translating the physical energy from a person plucking the strings, to electrical energy that is sent to an amplifier to create sound.


title: Bass guitar

text: Bass guitar strings are made up of two main components: the core and the winding. The core is the central wire that runs through the center of the string and is generally made up of steel, nickel or some alloy. The difference in material can have an effect on the sound of the bass guitar. There are four main methods of string winding: roundwound, flatwound, tapewound, and groundwound (half-round). The difference in winding also has an impact on the sound of the bass guitar, but the most commonly found strings is the roundwound, which involves the core wire being wrapped with another round-shaped wire.


title: Bass guitar

text: Roundwound strings are the most popular form of strings on bass guitars and are known for producing a tone with more harmonics. The next most common string found on bass guitars are flatwound strings. Flatwound strings are known for a smoother sound and feel compared to roundwound strings. Tapewound strings are similar to flatwound strings except, tapewound strings are wrapped in a non-metal material, such as nylon, giving an even slicker feel and a fuzzier tone.


title: Bass guitar

text: In the 1930s, musician and inventor Paul Tutmarc of Seattle, Washington, developed the first electric bass guitar in its modern form, a fretted instrument designed to be played horizontally. The 1935 sales catalog for Tutmarc's company Audiovox featured his "Model 736 Bass Fiddle", a solid-bodied electric bass guitar with four strings, a scale length, and a single pickup. Around 100 were made during this period.


title: Bass guitar

text: In the 1950s, Leo Fender and George Fullerton developed the first mass-produced electric bass guitar. The Fender Electric Instrument Manufacturing Company began producing the Precision Bass, or P-Bass, in October 1951. The design featured a simple uncontoured "slab" body design and a single coil pickup similar to that of a Telecaster. By 1957 the Precision more closely resembled the Fender Stratocaster with the body edges beveled for comfort, and the pickup was changed to a split coil design.


title: Bass guitar

text: The Fender Bass was a revolutionary instrument for gigging musicians. In comparison with the large, heavy upright bass, which had been the main bass instrument in popular music from the early 20th century to the 1940s, the bass guitar could be easily transported to shows. When amplified, the bass guitar was also less prone than acoustic basses to unwanted audio feedback. The addition of frets enabled bassists to play in tune more easily than on fretless acoustic or electric upright basses, and allowed guitarists to more easily transition to the instrument.


title: Bass guitar

text: In 1953, Monk Montgomery became the first bassist to tour with the Fender bass, in Lionel Hampton's postwar big band. Montgomery was also possibly the first to record with the electric bass, on July 2, 1953, with the Art Farmer Septet. Roy Johnson (with Lionel Hampton), and Shifty Henry (with Louis Jordan and His Tympany Five), were other early Fender bass pioneers. Bill Black, who played with Elvis Presley, switched from upright bass to the Fender Precision Bass around 1957. The bass guitar was intended to appeal to guitarists as well as upright bass players, and many early pioneers of the instrument, such as Carol Kaye, Joe Osborn, and Paul McCartney were originally guitarists.


title: Bass guitar

text: Also in 1953, Gibson released the first short-scale violin-shaped electric bass, the EB-1, with an extendable end pin so a bassist could play it upright or horizontally. In 1958, Gibson released the maple arched-top EB-2 described in the Gibson catalog as a "hollow-body electric bass that features a Bass/Baritone pushbutton for two different tonal characteristics". In 1959, these were followed by the more conventional-looking EB-0 Bass. The EB-0 was very similar to a Gibson SG in appearance (although the earliest examples have a slab-sided body shape closer to that of the double-cutaway Les Paul Special). The Fender and Gibson versions used bolt-on and set necks.


title: Bass guitar

text: Several other companies also began manufacturing bass guitars during the 1950s. 1956 saw the appearance at the German trade fair "Musikmesse Frankfurt" of the distinctive Höfner 500/1 violin-shaped bass, made using violin construction techniques by Walter Höfner, a second-generation violin luthier. Due to its use by Paul McCartney, it became known as the "Beatle bass". In 1957, Rickenbacker introduced the model 4000, the first bass to feature a neck-through-body design in which the neck is part of the body wood. Kay Musical Instrument Company began production of the K-162 in 1952, Danelectro released the Longhorn in 1956, and Burns London/Supersound in 1958.


title: Bass guitar

text: With the explosion in popularity of rock music in the 1960s, many more manufacturers began making electric basses, including Yamaha, Teisco and Guyatone. Introduced in 1960, the Fender Jazz Bass, initially known as the "Deluxe Bass", used a body design known as an offset waist which was first seen on the Jazzmaster guitar in an effort to improve comfort while playing seated. The J-bass features two single-coil pickups.


title: Bass guitar

text: Providing a more "Gibson-scale" instrument, rather than the Jazz and Precision, Fender produced the Mustang Bass, a scale-length instrument. The Fender VI, a 6 string bass, was tuned one octave lower than standard guitar tuning. It was released in 1961, and was briefly favored by Jack Bruce of Cream.


title: Bass guitar

text: Gibson introduced its short-scale EB-3 in 1961, also used by Bruce. The EB-3 had a "mini-humbucker" at the bridge position. Gibson basses tended to be instruments with a shorter 30.5" scale length than the Precision. Gibson did not produce a -scale bass until 1963 with the release of the Thunderbird.


title: Bass guitar

text: The first commercial fretless bass guitar was the Ampeg AUB-1, introduced in 1966. In the late 1960s, eight-string basses, with four octave paired courses (similar to a 12 string guitar), were introduced, such as the Hagström H8.


title: Bass guitar

text: In 1972, Alembic established what became known as "boutique" or "high-end" electric bass guitars. These expensive, custom-tailored instruments, as used by Phil Lesh, Jack Casady, and Stanley Clarke, featured unique designs, premium hand-finished wood bodies, and innovative construction techniques such as multi-laminate neck-through-body construction and graphite necks. Alembic also pioneered the use of onboard electronics for pre-amplification and equalization. Active electronics increase the output of the instrument, and allow more options for controlling tonal flexibility, giving the player the ability to amplify as well as to attenuate certain frequency ranges while improving the overall frequency response (including more low-register and high-register sounds). 1976 saw the UK company Wal begin production of their own range of active basses. In 1974 Music Man Instruments, founded by Tom Walker, Forrest White and Leo Fender, introduced the StingRay, the first widely produced bass with active (powered) electronics built into the instrument. Basses with active electronics can include a preamplifier and knobs for boosting and cutting the low and high frequencies.


title: Bass guitar

text: In the mid-1970s, five-string basses, with a very low "B" string, were introduced. In 1975, bassist Anthony Jackson commissioned luthier Carl Thompson to build a six-string bass tuned (low to high) B0, E1, A1, D2, G2, C3, adding a low B string and a high C string.


title: Bass guitar

text: While electric bass guitars are traditionally fretted instruments, fretless bass guitars are used by some players to achieve different tones, as well as playing additional micro tones. In 1961, Rolling Stones bassist Bill Wyman converted a used UK-built Dallas Tuxedo bass by removing the frets and filling in the slots with wood putty.


title: Maximum likelihood estimation

text: In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.


title: Maximum likelihood estimation

text: If the likelihood function is differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when all observed outcomes are assumed to have Normal distributions with the same variance.


title: Maximum likelihood estimation

text: From the perspective of Bayesian inference, MLE is generally equivalent to maximum a posteriori (MAP) estimation with uniform prior distributions (or a normal prior distribution with a standard deviation of infinity). In frequentist inference, MLE is a special case of an extremum estimator, with the objective function being the likelihood.


title: Maximum likelihood estimation

text: We model a set of observations as a random sample from an unknown joint probability distribution which is expressed in terms of a set of parameters. The goal of maximum likelihood estimation is to determine the parameters for which the observed data have the highest joint probability. We write the parameters governing the joint distribution as a vector formula_1 so that this distribution falls within a parametric family formula_2 where formula_3 is called the "parameter space", a finite-dimensional subset of Euclidean space. Evaluating the joint density at the observed data sample formula_4 gives a real-valued function,


title: Maximum likelihood estimation

text: which is called the likelihood function. For independent and identically distributed random variables, formula_6 will be the product of univariate density functions:


title: Maximum likelihood estimation

text: The goal of maximum likelihood estimation is to find the values of the model parameters that maximize the likelihood function over the parameter space, that is


title: Maximum likelihood estimation

text: Intuitively, this selects the parameter values that make the observed data most probable. The specific value formula_9 that maximizes the likelihood function formula_10 is called the maximum likelihood estimate. Further, if the function formula_11 so defined is measurable, then it is called the maximum likelihood estimator. It is generally a function defined over the sample space, i.e. taking a given sample as its argument. A sufficient but not necessary condition for its existence is for the likelihood function to be continuous over a parameter space formula_3 that is compact. For an open formula_3 the likelihood function may increase without ever reaching a supremum value.


title: Maximum likelihood estimation

text: In practice, it is often convenient to work with the natural logarithm of the likelihood function, called the log-likelihood:


title: Maximum likelihood estimation

text: Since the logarithm is a monotonic function, the maximum of formula_15 occurs at the same value of formula_16 as does the maximum of formula_17 If formula_18 is differentiable in formula_19 the necessary conditions for the occurrence of a maximum (or a minimum) are


title: Maximum likelihood estimation

text: known as the likelihood equations. For some models, these equations can be explicitly solved for formula_21 but in general no closed-form solution to the maximization problem is known or available, and an MLE can only be found via numerical optimization. Another problem is that in finite samples, there may exist multiple roots for the likelihood equations. Whether the identified root formula_22 of the likelihood equations is indeed a (local) maximum depends on whether the matrix of second-order partial and cross-partial derivatives, the so-called Hessian matrix


title: Maximum likelihood estimation

text: is negative semi-definite at formula_24, as this indicates local concavity. Conveniently, most common probability distributions – in particular the exponential family – are logarithmically concave.


title: Maximum likelihood estimation

text: While the domain of the likelihood function—the parameter space—is generally a finite-dimensional subset of Euclidean space, additional restrictions sometimes need to be incorporated into the estimation process. The parameter space can be expressed as


title: Maximum likelihood estimation

text: where formula_26 is a vector-valued function mapping formula_27 into formula_28 Estimating the true parameter formula_16 belonging to formula_30 then, as a practical matter, means to find the maximum of the likelihood function subject to the constraint formula_31


title: Maximum likelihood estimation

text: Theoretically, the most natural approach to this constrained optimization problem is the method of substitution, that is "filling out" the restrictions formula_32 to a set formula_33 in such a way that formula_34 is a one-to-one function from formula_35 to itself, and reparameterize the likelihood function by setting formula_36 Because of the equivariance of the maximum likelihood estimator, the properties of the MLE apply to the restricted estimates also. For instance, in a multivariate normal distribution the covariance matrix formula_37 must be positive-definite; this restriction can be imposed by replacing formula_38 where formula_39 is a real upper triangular matrix and formula_40 is its transpose.


title: Maximum likelihood estimation

text: In practice, restrictions are usually imposed using the method of Lagrange which, given the constraints as defined above, leads to the "restricted likelihood equations"


title: Maximum likelihood estimation

text: where formula_43 is a column-vector of Lagrange multipliers and formula_44 is the Jacobian matrix of partial derivatives. Naturally, if the constraints are not binding at the maximum, the Lagrange multipliers should be zero. This in turn allows for a statistical test of the "validity" of the constraint, known as the Lagrange multiplier test.


title: Maximum likelihood estimation

text: A maximum likelihood estimator is an extremum estimator obtained by maximizing, as a function of "θ", the objective function formula_45. If the data are independent and identically distributed, then we have


title: Maximum likelihood estimation

text: this being the sample analogue of the expected log-likelihood formula_47, where this expectation is taken with respect to the true density.


title: Maximum likelihood estimation

text: Maximum-likelihood estimators have no optimum properties for finite samples, in the sense that (when evaluated on finite samples) other estimators may have greater concentration around the true parameter-value. However, like other estimation methods, maximum likelihood estimation possesses a number of attractive limiting properties: As the sample size increases to infinity, sequences of maximum likelihood estimators have these properties:


title: Maximum likelihood estimation

text: Under the conditions outlined below, the maximum likelihood estimator is consistent. The consistency means that if the data were generated by formula_54 and we have a sufficiently large number of observations "n", then it is possible to find the value of "θ" with arbitrary precision. In mathematical terms this means that as "n" goes to infinity the estimator formula_24 converges in probability to its true value:


title: Maximum likelihood estimation

text: In practical applications, data is never generated by formula_54. Rather, formula_54 is a model, often in idealized form, of the process generated by the data. It is a common aphorism in statistics that "all models are wrong". Thus, true consistency does not occur in practical applications. Nevertheless, consistency is often considered to be a desirable property for an estimator to have.


title: Maximum likelihood estimation

text: The dominance condition can be employed in the case of i.i.d. observations. In the non-i.i.d. case, the uniform convergence in probability can be checked by showing that the sequence formula_60 is stochastically equicontinuous.


title: Maximum likelihood estimation

text: If one wants to demonstrate that the ML estimator formula_24 converges to "θ" almost surely, then a stronger condition of uniform convergence almost surely has to be imposed:


title: Maximum likelihood estimation

text: Additionally, if (as assumed above) the data were generated by formula_54, then under certain conditions, it can also be shown that the maximum likelihood estimator converges in distribution to a normal distribution. Specifically,


title: Maximum likelihood estimation

text: The maximum likelihood estimator selects the parameter value which gives the observed data the largest possible probability (or probability density, in the continuous case). If the parameter consists of a number of components, then we define their separate maximum likelihood estimators, as the corresponding component of the MLE of the complete parameter. Consistent with this, if formula_24 is the MLE for formula_16, and if formula_67 is any transformation of formula_16, then the MLE for formula_69 is by definition


title: Maximum likelihood estimation

text: The MLE is also equivariant with respect to certain transformations of the data. If formula_72 where formula_73 is one to one and does not depend on the parameters to be estimated, then the density functions satisfy


title: Maximum likelihood estimation

text: and hence the likelihood functions for formula_75 and formula_76 differ only by a factor that does not depend on the model parameters.


title: Maximum likelihood estimation

text: For example, the MLE parameters of the log-normal distribution are the same as those of the normal distribution fitted to the logarithm of the data.


title: Maximum likelihood estimation

text: As assumed above, if the data were generated by formula_77 then under certain conditions, it can also be shown that the maximum likelihood estimator converges in distribution to a normal distribution. It is -consistent and asymptotically efficient, meaning that it reaches the Cramér–Rao bound. Specifically,


title: Maximum likelihood estimation

text: In particular, it means that the bias of the maximum likelihood estimator is equal to zero up to the order .


title: Maximum likelihood estimation

text: However, when we consider the higher-order terms in the expansion of the distribution of this estimator, it turns out that has bias of order . This bias is equal to (componentwise)


title: Maximum likelihood estimation

text: where formula_82 (with superscripts) denotes the ("j,k")-th component of the "inverse" Fisher information matrix formula_83, and


title: Maximum likelihood estimation

text: Using these formulae it is possible to estimate the second-order bias of the maximum likelihood estimator, and "correct" for that bias by subtracting it:


title: Maximum likelihood estimation

text: This estimator is unbiased up to the terms of order , and is called the bias-corrected maximum likelihood estimator.


title: Maximum likelihood estimation

text: This bias-corrected estimator is (at least within the curved exponential family), meaning that it has minimal mean squared error among all second-order bias-corrected estimators, up to the terms of the order  . It is possible to continue this process, that is to derive the third-order bias-correction term, and so on. However, the maximum likelihood estimator is "not" third-order efficient.


title: Maximum likelihood estimation

text: A maximum likelihood estimator coincides with the most probable Bayesian estimator given a uniform prior distribution on the parameters. Indeed, the maximum a posteriori estimate is the parameter that maximizes the probability of given the data, given by Bayes' theorem:


title: Maximum likelihood estimation

text: where formula_87 is the prior distribution for the parameter and where formula_88 is the probability of the data averaged over all parameters. Since the denominator is independent of , the Bayesian estimator is obtained by maximizing formula_89 with respect to . If we further assume that the prior formula_87 is a uniform distribution, the Bayesian estimator is obtained by maximizing the likelihood function formula_91. Thus the Bayesian estimator coincides with the maximum likelihood estimator for a uniform prior distribution formula_87.


title: Maximum likelihood estimation

text: In many practical applications in machine learning, maximum-likelihood estimation is used as the model for parameter estimation.


title: Maximum likelihood estimation

text: The Bayesian Decision theory is about designing a classifier that minimizes total expected risk, especially, when the costs (the loss function) associated with different decisions are equal, the classifier is minimizing the error over the whole distribution.


title: Maximum likelihood estimation

text: where formula_96 are predictions of different classes. From a perspective of minimizing error, it can also be stated as


title: Maximum likelihood estimation

text: and if we further assume the zero-or-one loss function, which is a same loss for all errors, the Bayes Decision rule can be reformulated as:


title: Maximum likelihood estimation

text: Finding formula_106 that maximizes the likelihood is asymptotically equivalent to finding the formula_106 that defines a probability distribution (formula_108) that has a minimal distance, in terms of Kullback–Leibler divergence, to the real probability distribution from which our data were generated (i.e., generated by formula_109). In an ideal world, P and Q are the same (and the only thing unknown is formula_16 that defines P), but even if they are not and the model we use is misspecified, still the MLE will give us the "closest" distribution (within the restriction of a model Q that depends on formula_106) to the real distribution formula_109.


title: Maximum likelihood estimation

text: Since cross entropy is just Shannon's entropy plus KL divergence, and since the entropy of formula_109 is constant, then the MLE is also asymptotically minimizing cross entropy.


title: Maximum likelihood estimation

text: Consider a case where "n" tickets numbered from 1 to "n" are placed in a box and one is selected at random ("see uniform distribution"); thus, the sample size is 1. If "n" is unknown, then the maximum likelihood estimator formula_114 of "n" is the number "m" on the drawn ticket. (The likelihood is 0 for "n" < "m", for "n" ≥ "m", and this is greatest when "n" = "m". Note that the maximum likelihood estimate of "n" occurs at the lower extreme of possible values {"m", "m" + 1, ...}, rather than somewhere in the "middle" of the range of possible values, which would result in less bias.) The expected value of the number "m" on the drawn ticket, and therefore the expected value of formula_114, is ("n" + 1)/2. As a result, with a sample size of 1, the maximum likelihood estimator for "n" will systematically underestimate "n" by ("n" − 1)/2.


title: Maximum likelihood estimation

text: Suppose one wishes to determine just how biased an unfair coin is. Call the probability of tossing a ‘head’ "p". The goal then becomes to determine "p".


title: Maximum likelihood estimation

text: Suppose the coin is tossed 80 times: i.e. the sample might be something like "x" = H, "x" = T, ..., "x" = T, and the count of the number of heads "H" is observed.


title: Maximum likelihood estimation

text: The probability of tossing tails is 1 − "p" (so here "p" is "θ" above). Suppose the outcome is 49 heads and 31 tails, and suppose the coin was taken from a box containing three coins: one which gives heads with probability "p" = , one which gives heads with probability "p" =  and another which gives heads with probability "p" = . The coins have lost their labels, so which one it was is unknown. Using maximum likelihood estimation, the coin that has the largest likelihood can be found, given the data that were observed. By using the probability mass function of the binomial distribution with sample size equal to 80, number successes equal to 49 but for different values of "p" (the "probability of success"), the likelihood function (defined below) takes one of three values:


title: Maximum likelihood estimation

text: Now suppose that there was only one coin but its could have been any value The likelihood function to be maximised is


title: Maximum likelihood estimation

text: This is a product of three terms. The first term is 0 when  = 0. The second is 0 when  = 1. The third is zero when  = . The solution that maximizes the likelihood is clearly  =  (since  = 0 and  = 1 result in a likelihood of 0). Thus the "maximum likelihood estimator" for is .


title: Maximum likelihood estimation

text: This result is easily generalized by substituting a letter such as in the place of 49 to represent the observed number of 'successes' of our Bernoulli trials, and a letter such as in the place of 80 to represent the number of Bernoulli trials. Exactly the same calculation yields which is the maximum likelihood estimator for any sequence of Bernoulli trials resulting in 'successes'.


title: Maximum likelihood estimation

text: the corresponding probability density function for a sample of independent identically distributed normal random variables (the likelihood) is


title: Maximum likelihood estimation

text: This family of distributions has two parameters: ; so we maximize the likelihood, formula_122, over both parameters simultaneously, or if possible, individually.


title: Maximum likelihood estimation

text: Since the logarithm function itself is a continuous strictly increasing function over the range of the likelihood, the values which maximize the likelihood will also maximize its logarithm (the log-likelihood itself is not necessarily strictly increasing). The log-likelihood can be written as follows:


title: Maximum likelihood estimation

text: This is indeed the maximum of the function, since it is the only turning point in and the second derivative is strictly less than zero. Its expected value is equal to the parameter of the given distribution,


title: Maximum likelihood estimation

text: To calculate its expected value, it is convenient to rewrite the expression in terms of zero-mean random variables (statistical error) formula_133. Expressing the estimate in these variables yields


title: Maximum likelihood estimation

text: Simplifying the expression above, utilizing the facts that formula_135 and formula_136, allows us to obtain


title: Maximum likelihood estimation

text: This means that the estimator formula_138 is biased for formula_139. It can also be shown that formula_140 is biased for formula_141, but that both formula_138 and formula_140 are consistent.


title: Maximum likelihood estimation

text: In this case the MLEs could be obtained individually. In general this may not be the case, and the MLEs would have to be obtained simultaneously.


title: Maximum likelihood estimation

text: This maximum log-likelihood can be shown to be the same for more general least squares, even for non-linear least squares. This is often used in determining likelihood-based approximate confidence intervals and confidence regions, which are generally more accurate than those using the asymptotic normality discussed above.


title: Maximum likelihood estimation

text: It may be the case that variables are correlated, that is, not independent. Two random variables formula_147 and formula_148 are independent only if their joint probability density function is the product of the individual probability density functions, i.e.


title: Maximum likelihood estimation

text: Suppose one constructs an order-"n" Gaussian vector out of random variables formula_150, where each variable has means given by formula_151. Furthermore, let the covariance matrix be denoted by formula_152. The joint probability density function of these "n" random variables then follows a multivariate normal distribution given by:


title: Maximum likelihood estimation

text: In this and other cases where a joint density function exists, the likelihood function is defined as above, in the section "principles," using this density.


title: Maximum likelihood estimation

text: formula_155 are counts in cells / boxes 1 up to m; each box has a different probability (think of the boxes being bigger or smaller) and we fix the number of balls that fall to be formula_156:formula_157. The probability of each box is formula_158, with a constraint: formula_159. This is a case in which the formula_160 "s" are not independent, the joint probability of a vector formula_161 is called the multinomial and has the form:


title: Maximum likelihood estimation

text: Each box taken separately against all the other boxes is a binomial and this is an extension thereof.


title: Maximum likelihood estimation

text: Maximizing log likelihood, with and without constraints, can be an unsolvable problem in closed form, then we have to use iterative procedures.


title: Maximum likelihood estimation

text: cannot be solved explicitly for an estimator formula_167. Instead, they need to be solved iteratively: starting from an initial guess of formula_16 (say formula_169), one seeks to obtain a convergent sequence formula_170. Many methods for this kind of optimization problem are available, but the most commonly used ones are algorithms based on an updating formula of the form


title: Maximum likelihood estimation

text: where the vector formula_172 indicates the descent direction of the rth "step," and the scalar formula_173 captures the "step length," also known as the learning rate.


title: Maximum likelihood estimation

text: Gradient descent method requires to calculate the gradient at the rth iteration, but no need to calculate the inverse of second-order derivative, i.e., the Hessian matrix. Therefore, it is computationally faster than Newton-Raphson method.


title: Maximum likelihood estimation

text: where formula_178 is the score and formula_179 is the inverse of the Hessian matrix of the log-likelihood function, both evaluated the rth iteration. But because the calculation of the Hessian matrix is computationally costly, numerous alternatives have been proposed. The popular Berndt–Hall–Hall–Hausman algorithm approximates the Hessian with the outer product of the expected gradient, such that


title: Maximum likelihood estimation

text: Other quasi-Newton methods use more elaborate secant updates to give approximation of Hessian matrix.


title: Maximum likelihood estimation

text: DFP formula finds a solution that is symmetric, positive-definite and closest to the current approximate value of second-order derivative:


title: Maximum likelihood estimation

text: BFGS method is not guaranteed to converge unless the function has a quadratic Taylor expansion near an optimum. However, BFGS can have acceptable performance even for non-smooth optimization instances


title: Maximum likelihood estimation

text: Another popular method is to replace the Hessian with the Fisher information matrix, formula_188, giving us the Fisher scoring algorithm. This procedure is standard in the estimation of many methods, such as generalized linear models.


title: Maximum likelihood estimation

text: Although popular, quasi-Newton methods may converge to a stationary point that is not necessarily a local or global maximum, but rather a local minimum or a saddle point. Therefore, it is important to assess the validity of the obtained solution to the likelihood equations, by verifying that the Hessian, evaluated at the solution, is both negative definite and well-conditioned.


title: Maximum likelihood estimation

text: Early users of maximum likelihood were Carl Friedrich Gauss, Pierre-Simon Laplace, Thorvald N. Thiele, and Francis Ysidro Edgeworth. However, its widespread use rose between 1912 and 1922 when Ronald Fisher recommended, widely popularized, and carefully analyzed maximum-likelihood estimation (with fruitless attempts at proofs).


title: Maximum likelihood estimation

text: Maximum-likelihood estimation finally transcended heuristic justification in a proof published by Samuel S. Wilks in 1938, now called Wilks' theorem. The theorem shows that the error in the logarithm of likelihood values for estimates from multiple independent observations is asymptotically "χ"-distributed, which enables convenient determination of a confidence region around any estimate of the parameters. The only difficult part of Wilks’ proof depends on the expected value of the Fisher information matrix, which is provided by a theorem proven by Fisher. Wilks continued to improve on the generality of the theorem throughout his life, with his most general proof published in 1962.


title: Maximum likelihood estimation

text: Reviews of the development of maximum likelihood estimation have been provided by a number of authors.


title: Wrestling

text: Wrestling is a series of combat sports involving grappling-type techniques such as clinch fighting, throws and takedowns, joint locks, pins and other grappling holds. Wrestling techniques have been incorporated into martial arts, combat sports and military systems. The sport can either be genuinely competitive or sportive entertainment (see professional wrestling).


title: Wrestling

text: Wrestling comes in different forms such as freestyle, Greco-Roman, judo, sambo, folkstyle, catch, submission, sumo, pehlwani, shuai jiao and others. A wrestling bout is a physical competition, between two (sometimes more) competitors or sparring partners, who attempt to gain and maintain a superior position.


title: Wrestling

text: There are a wide range of styles with varying rules, with both traditional historic and modern styles. The term "wrestling" is attested in late Old English, as "wræstlunge" (glossing "palestram").


title: Wrestling

text: Wrestling represents one of the oldest forms of combat. The origins of wrestling go back 15,000 years through cave drawings in France. Babylonian and Egyptian reliefs show wrestlers using most of the holds known in the present-day sport. Literary references to it occur as early as the Old Testament and the ancient Indian Vedas. In the Book of Genesis, the Patriarch Jacob is said to have wrestled with God or an angel. The Iliad, in which Homer recounts the Trojan War of the 13th or 12th century BC, also contains mentions of wrestling. Indian epics Ramayana and Mahabharata contain references to martial arts including wrestling.


title: Wrestling

text: In Ancient Greece wrestling occupied a prominent place in legend, literature and philosophy. Wrestling competition, brutal in many aspects, served as the focal sport of the ancient Olympic Games. Ancient Romans borrowed heavily from Greek wrestling, but eliminated much of its brutality. Wrestling is referenced throughout both Ancient Greek and Roman literature. Many philosophers and leaders practiced wrestling and/or referenced the sport frequently in their works, most notably Plato, Socrates, Aristotle, Xenophon, Epictetus, Seneca, Plutarch and Marcus Aurelius. Dicaearchus wrote that Plato wrestled at the Isthmian games. Many of Plato's dialogues are set in wrestling schools. Ancient Greek lyric poet Pindar wrote victory odes, grouped into four books named after the Olympian, Pythian, Isthmian, and Nemean GamesPanhellenic festivals held respectively at Olympia, Delphi, Corinth and Nemea. These odes were composed to honor the men and youths who had enjoyed victories in wrestling, boxing, pankration and other athletic contests.


title: Wrestling

text: During the Middle Ages (fifth century to fifteenth century) wrestling remained popular and enjoyed the patronage of many royal families, including those of France, Japan and England.