recording. Okay, the class is in session and we are recording. Welcome once again, guys. Let's get started right away. Can I request any one of us to just start us off with the word of prayer, get into it. Pastor, can I pray? Yes, please. Go ahead. Okay. Heavenly Father, we are grateful once again for this morning and for this opportunity to bring us all back from our various nations and our tribes and our homes. Father, we praise your holy name for your grace that has abound with us throughout our holidays. Father, we commit ourselves into the gracious hands once again. As we are beginning a new academic semester, we pray that your grace continue to be sufficient with us in the name of Jesus. Father, we pray that, Lord, you supply all our needs according to your glorious riches in the name of Jesus. Father, we commit, Lord, our first, our teacher, pastoration into your mighty hands of God. Continue to keep him and guide him in the name of Jesus. Father, whatever that you inspire him to teach us may it be a blessing unto us in the name of Jesus. Father, I pray that you grant him the utterances that each day when we encounter him, we will understand him and he will also be able to pour out whatever you have deposited in him into us in the name of Jesus.  Father, I pray for understanding. I pray for the ability to be able to comprehend whatever you will be taught in this class and we can put it into practical ministry in the name of Jesus. We thank you for an answered prayer, oh God. In Jesus' mighty name we pray. Amen. Amen. Amen. Thank you, Elisha. Thanks, everyone. Once again, as mentioned, it's just lovely to connect with you all. I think I saw you somewhere. Good to see you. Right, so this course, let me go ahead and share the screen. We can all see the screen. So this is BC 311, a worship ministry. It's the third year course and just to give you a brief overview of what this course is all about. It's going to be, it's going to provide a very important and practical, you know, on how you organize, lead, develop and pastor the worship ministry in a local church. A lot of the experiences and some of the methods will be shared from how we do things at APC here in Bangalore, India. But this is what the course is all about is... Yeah, it's all about giving us a more of a practical understanding of how we can, you know, approach this worship ministry as we call it. So, but we will be just starting off from where we left off with regards to appraisal and worship from our first year course. You know, we, towards the very end, we learned the importance of corporate worship and also the regional worship, right? So just for us to start us off is to go through the course outline. We'll be looking at worship ministry in the Bible. To start off, we will learn a little bit, once again, about worship and how it was organized in the Bible. The Old Testament and in the New Testament. And then we'll go through a brief journey through time and see how worship movement or the sound or the expression of worship and singing has evolved through time. And then get more deeper into the practical aspects of worship ministry. You know, what are the roles and the responsibilities, how the organizational aspect of it and the spiritual aspects, what is expected of every team member in the worship ministry and team. The technology that is used in worship ministry, what can be used and some suggestions for you to take. Maybe if you're leading a church or any ministry, you can hoping that it would be helpful and some of the technology that will be suggested as well. And then developing a local community as a worshiping body and the importance of regional language expressions of worship. Okay, so this is what this course is all about and most of you are expecting already and so let's get right into it. Right, so the first chapter we look at is worship ministry in the Bible and one of the people that I'd like to start off by looking at is Abraham. Abraham was known many things. He's known as the father of faith and whatnot. And one of the things that he is known for very popularly in the Christian circle amongst worshipers and churches is that he was the man of altars. So that's what we're going to look at briefly today is the altars of Abraham. The altars of Abraham. But so before we just dive into it, when you hear the word Abraham, the person and then his name Abraham, what stands out to you? What is the first impression of Abraham for you? Okay, let me know in the chat section. Can I say something? Sure, sure. Yes. Yeah, my first impression about Abraham is faith. Yeah, that he's a man of faith and the majorly and then I hear of him beginning altars from nowhere. He had never seen any canonite or what? That was being altars, but he begins altars and then remember he's coming from a family which was serving other gods. Maybe he was basing on the altars of their gods. I don't know, but that's what comes in my mind. Thank you. Thanks Charles. Yeah, thanks guys for sharing in the chat section. I see lovely surrendered to God, father of faith, man of faith. It's called to be a friend of God, man of faith and prayers. A man of radical faith, obedience. That's interesting. Air of the world. Okay. Yeah, I mean, there's so much that can be spoken of about Abraham, isn't it? About our father of faith. There's so many things and if we have to do a character study on his life and the revelation is amazing and it never ceases to amaze us and intercessor as well. But so the one aspect we'd like to look in this session is that he was the man of altars as well, right? He built altars. So yeah, let's get started. So when God calls Abraham and we know it's the very famous chapter where we all know that it's almost I'm preaching to the choir here, but teaching to the choir. I'm preaching. We know Genesis chapter 12 until Genesis 11. Genesis 12 takes a such a drastic 180 degree turn per se from all of a sudden from all the failures of human and humans and human history and so many people and generations. And suddenly in Genesis chapter 12, the focus is turned to one man, right? It's just brilliant. It's just so interesting. And God calls Abraham. He tells him leave his land, his relatives, his family, his father's house and go to the land that he will show. That's what God says, right?  So that means he didn't fully have a revelation of the big picture Abraham did not have. This is where I'm going to go. Google Maps from here to there. How many kilometers? How many restaurants in the middle? Where can I take my break? Where can I stop for? Where can I fill fuel? Nothing, right? Yeah, we've all traveled and we've all used Google Maps. So you know what I'm talking about, right?  Sometimes not all of us plan, but right. And so throughout his journey, Abraham built four altars and they represent the stages of his experience as you can see in your notes and growth in the faith. They represent the stages of a different stage of his experience, his walk, his progress and growth in the faith. They show how he behaved himself in a manner that not only commended him to the Lord, but that clearly demonstrated his commitment to a walk of faith with his God. Okay, but what we have to remember when God calls Abraham, he was coming from a polytheistic religion. Polytheistic means you have many gods, right? And he was an idol worshiper. He comes from a region and from amongst people was an idol worshiper, right? And so that's the background, the setting that God calls him up and asks him to go on a journey. Okay, I just want to stop sharing the notes for just one quick second and share a tab here for us to... Okay, so we can see this map here, right? So this is where he was, Ur, right? This is where Abraham used to live. It was the land of the Chaldeans, right? The meaning of Ur, some say it was the moonlit city or light, so city of lights, something like that. But this is where he was. And so you see here the red line shows Abraham's journey. So the journey of Isaac, Jacob, we... let's ignore the purple, blue and the brown. Okay, let's look at the red line. So it goes all the way from here. It's going, Babylon is coming, it's coming, it's going, it's going. Okay, this is brown, but he's going up north again to Haran and then takes a diversion. It's down south, it's coming all the way down, all the way down here to Damascus and then he comes here and shake him. Now you... as we go, you will see this is where he first builds the altar, okay? But we'll see. We'll read the scriptures as well, but I just wanted us to just have a picture of this. Shake him to Bethel, coming down. If you come down south, Hebron, Kadesh, and then Shur, and all the way to Egypt, okay? So we will... you all know that Abraham went to Egypt as well. This is the land of Goshen just for our understanding. This is where during the time of Exodus, Moses, this is where the Israelites were in Egypt. This is the land of Goshen. Once again, you all know, we are aware of that, right? It's quite an incredible journey, isn't it? I mean, just looking at a map, it gives us a different perspective altogether. Yeah, okay. I think I'll leave that map as it is just for us to have a picture of. But in the meantime, also, I'm also hoping that you have your notes open on your screens just so we can follow along, right? Okay, so Abraham, in this chapter, what we're learning is that he was the man of altars. And as most of you have expressed that he was a man of obedience, he trusted God and obeyed. He was a father of faith, man of faith, friend of God, et cetera, et cetera. And now we know that he was a man of altars. And when you hear the word altar, what's the first thing that comes to your mind?  Can I say something? This is Charles. Charles, go ahead, yeah.  Humanity meets divinity. Sacrifice and prayer, sacrifice, right? Covenant, yeah, thank you, Saddam. Place of sacrifice, thanks, Avani.  Okay, reminder that you're ransomed, redeemed, yeah. In the very, one of the first times that you will come across the word altar is after the fall, when the narrative turns towards Cain and Abel worship. The first thing we see is that they built an altar, right? So as Charles also said, the altar initially was a bridge, it was a common place. It was a meeting place to bridge the great divorce that had happened because of sin. It is, again, to, I can't say better than what Charles said, it's where humanity met with divinity, or divinity met with humanity. Right, it was a common place. It was a meeting place. That was the altar. And then we know that, you know, humans populated, the population increased and whatnot. And then in the scripture, if you look at the notes, the word altar in scripture means a place of slaughter and sacrifice, where bloodshed and death took place. It symbolized acknowledgement of or approach to and appreciation of God. In other words, worship.  It was a place of slaughter and sacrifice.  It symbolized, that's where you acknowledged who God is, who God was. And some more pointers there is primarily an altar was a place of worship, where God was adored for who he is and what he has done. Okay, it was a place of worship to adore him for who he is and what he has done. Only burnt offerings were offered to him in the days of the patriarchs since the law of Moses was not yet given. Okay, and altar was also a place of testimony to the only true God in the midst of widespread idolatry. So fast forward to the days of, you know, Abraham and all the way from this land of Ur and also in the land of Canaanites, Canaanites here, right, there were all idol worshipers. That means they had also learned that, okay, one way of worship or expressing worship is to build altars. So they had also built altars for their idols, false altars of worship, as we call it, right. And also was a place of communion between God and the worshipper where instructions were often given by the Lord and received by his servant. Okay, and everything else what you guys said, okay, so please know that in every point that is there, it's not the end of the list. Okay, it's not an exhaustive list. Everything that you've mentioned, like Thanksgiving table of sacrifice, ransom prayer and worship, place of sacrifice and covenant and whatnot. All of that is true. Okay, so now that we have understand who Abraham was, his background, his journey. Sorry. Christopher, yes, sorry, go ahead. Yeah, just a question, I mean, just a bit of curiosity over here. In those days, what really sort of motivated the people to sacrifice an animal, shed blood and kill a living animal? Yeah. And what sort of, how did that sort of translate to worship? Just sort of just curious, I mean, just curious why that, how that actually happened? Because I mean, just from a modern day perspective, when you talk about people who are not to eat animals and they don't, they feel that it's an ethical sort of reason that, you know, why people should not do that. Yeah, it's in many ways, partially an apologetic kind of a question, partially. But then I say that because we'll have to explain sin, right? Biblically, as when what is sin, the price of sin, the seriousness of sin, it basically, it means the wages of sin is death. And because of what had happened, because of the fall, everybody deserved death, we all deserve to die, right? But until and unless an innocent blood was shed, it had to be shed for us to live. And it was a reminder that I'm supposed to be on that altar, but instead of me, an innocent lamb or an animal is taking my place. So that's just a reminder of the seriousness of sin, of what and how serious God takes what, you know, that sin is serious. You know, it simply means death. And that's why, and also in response to Charles's questions, so the cross was an altar in a way that Jesus had to shed his blood and it is an altar, right? That Jesus was, as we read in Isaiah, he was an innocent lamb, a lamb with a blemish, a falseless, a perfect, sinless lamb of God. And then in the book of Hebrews, we see that Jesus was not only our offering, but he was also our offerer, right? He was not only our sacrifice, but he was also the high priest, right? With his own blood, he made a way for us by tearing the veil. So that's what it is. And like I said, you know, just how the practice of building altars was initiated. The first time we read in the Bible was with Cain and Abel, and then I'm sure as humanity grew, populated, they all understood, okay, the altar means it's a place of worship. And it's not like only until the first Jew, which is Abraham, the first Hebrew, rather, so to say, there was sacrifices happening with other religions as well and with other, you know, with false altars of worship. So yeah, I hope that explains just very briefly, but then about to explain that fully, Christopher, we need to explain sin and the person needs to understand the seriousness of sin. Right, thank you so much. Yeah, you're welcome. Hey, so I'll stop sharing the map. Actually, I'll just let the map be there so we can follow the PDF in your systems. Okay, so in page five of your notes, we see the first altar. In the notes, I'm calling it the altar of obedience. Okay, now there are, you can call it whatever you want to.  So from as I was preparing, from my perspective, this seemed like the altar of obedience. So I'm calling it the altar of obedience. Okay, so the first altar, let's see. But after Abraham arrived in Canon, the Bible tells us that the first place he went to was Shechem. And as you can see in the map where Shechem is. The Bible tells us that the first place he went to was Shechem. In Shechem, he built an altar. It is an altar associated with the proof of obedience, you know, proof of faith that Abraham took and whatnot. But very quickly, let's go to Genesis chapter 12 in your Bibles. Genesis chapter 12. Yeah, and I just want to read it for us. So it says, the lot said to Abraham, leave your country, your people and your father's household and go to the land. I will show you. Okay. I will make you into a great nation. I will bless you. I will make your name great and you will be a blessing.  And all peoples on earth will be blessed through you. And verse four. So Abraham, Abraham left. As the Lord had told him and lot his nephew went with him. Abram at this point was 75 years old when he set out from Haram. He took his wife, Sarai, his nephew, Lord, all the positions they had and accumulated and the people they had acquired in Haram. And they set out for the land of Canon. And they arrived there. For six. Abram traveled through the land as far as the site of the great tree of Moray at Shechem. At the time of Canonites were in the land. So he took his wife, Sarai, his nephew, Lord, all the positions they had accumulated and the people they had acquired in Haram. They set out for the land of Canon. And they arrived there. For six. Abram traveled through the land as far as the site of great tree of Moray at Shechem. At the time of Canonites were in the land. The Lord appeared to Abram and said, to your offspring, I will give this land. So he built an altar there to the Lord who appeared to him. Okay, verse six and seven. Pretty key. It's amazing how the narrative there stresses on the land at least three times. So they set out for the land of Canon. He traveled through the land. And then at that time Canonites were in the land. So land is pretty important. So verse seven, the Lord appeared to Abram and said to your offspring, I will give this land. So that is the land.  Okay, this is what I promised you. And this is what you and your descendants are getting. And there Abram's response was that he builds an altar. Okay, this is, and it's in line with what Hebrew chapter 11 verse eight says. It says, it was by faith that Abraham obeyed. When God called him to leave home and go to another land that God would give him as his inheritance. He went without knowing where he was going, right? He went without going where he was going. Sometimes we just need to pause, right? When we read things like this, although we are familiar with the life of Abraham and what he's done. And although we know that he is a father of faith, I think it's always good for us to slow down and pause and ask question ourselves here. Would we do that? When God says go, the natural tendency is what, where, when, why, how, who. All those philosophical questions will come up, isn't it? You know, I was talking about this land of Goshen here, right? You know, that you see, what was the challenge? What was one of the things that was making the Israelites uncomfortable, uncomfortable through their journey in the wilderness is the land of Goshen was a plane. Geographically, it means that you can see for a long distances. Like, you know, you can see people walking from a kilometer of variance because it's a plane, right? You can see what is ahead, what, where's the turn and whatnot. But when they came into the wilderness, as they were going through the wilderness, all of a sudden they don't know what's ahead. All they can see is these big hills and mountains in front of them. And they have to come to a certain point to turn. Okay. And this is where it turns left. This is where it turns right. And that's how we are in many cases, isn't it? We like to know what is ahead.  We get very anxious. We get very restless.  Okay, what's happening? What's happening? What's going to come tomorrow? You know, what tomorrow is going to look like? I don't know. But look at Abraham. Abraham, God told him to leave. He said, he left. He'll, you know, just took his wife, every, all of his cattle and whatnot, and he left. And then when he reached a certain place, God showed up to him and says, I'm going to give you this land. And there as a response, remember, guys, Abraham, right, is coming from a religion of a polytheistic religion. And then for him to leave all that, he was father's household, everything. And just come to a land as a foreigner, a stranger in a strange land as they say it. There he stops and he recognizes, okay, all right. This is, things are getting very real. And then as a response, he's building an altar. And remember, altar is just a place of worship, right? And in verse seven, it says, the Lord appeared to Abraham and said to your offspring, I will give this land. So he built an altar there to the Lord. Now, if you remember, one of the things that we learned in praise and worship class is worship is a response to an encounter with God. Remember that? Worship is a response to an encounter with God. What's happened here? Abraham is having an encounter with the Lord. He appeared to him and he's saying, you see this land? I'm going to give you this land into your descendants, to your offsprings. And so as a response, Abraham is building this altar. So we like to call this first altar as the altar of faith and obedience. And then as we go on, we see the second altar. Let's go to Genesis chapter 12 verse eight from there. Oh, just as a side note, guys, sorry. So this land of Shechem is a pretty important one in the history of Israelites as well. Just as a side note, I mean, there's a lot of references to it. But then very quickly, let's go. If you don't mind, if you can go to Joshua chapter 24, just remind it. Joshua chapter 24, where is it? Are you guys there? I feel they just say, yes, I'm there. I have arrived. I hope you guys are still with me. Okay. Joshua chapter 24 verse one onwards. It says, then Joshua assembled all the tribes of Israel at Shechem. Okay, look at that. Joshua assembled all the tribes of Israel at Shechem. Now, that means before Shechem, where were they? Like through the Exodus, the land of Egypt. So they come to the land that was given to them that God promised Abraham. Right. Finally, Joshua is the one who's led the Israelites after Moses into the promised land. And a lot has happened from Joshua chapter one to Joshua chapter 24. Then he says, then Joshua assembled all the tribes of Israel at Shechem. He summoned the elders, judges and officials of Israel. And they presented themselves before God. I'm just going to read a little bit. I hope it's okay because I just feel like it's important. Joshua said to all the people, this is what the Lord, the God of Israel says, long ago, your forefathers, including Tara, the father of Abraham and Nahor, lived beyond the river and worshiped other gods. They lived beyond the river. That means that another reference to the land of Ur is... So it was a city between two rivers. It was a city between two rivers. So that's the reference there. They lived beyond the river and worshiped other gods. But I took your father Abraham from the land beyond the river and led him throughout Canaan and gave him many descendants. I gave him Isaac and to Isaac I gave Jacob and Esau. I assigned the hill country of Sire to Esau. But Jacob and his sons went down to Egypt. Then I sent Moses and Aaron and I afflicted the Egyptians by what I did there. And I brought you out. When I brought your fathers out of Egypt, you came to the sea and the Egyptians pursued them with chariots and the horsemen as far as the Red Sea. But they cried out to the Lord for help and he put darkness between you and the Egyptians. He brought the sea over them and covered them. Just a very long passage short and come down all the way to verse 15 with me, please. Actually, let's go to verse 14. Now, fear the Lord and serve him with all faithfulness. Throw away other gods. Your forefathers worshiped beyond the river and in Egypt and serve the Lord. But if serving the Lord seems undesirable to you, then choose for yourselves this day whom you will serve. Whether the gods, your forefathers served beyond the river or the gods of the Amorites in whose land you are living. But as for me and my household, we will serve the Lord. Okay, if you pay close attention to the narrative, there's so many things to pay attention there. How many times he mentions, you know, your forefathers and the land beyond the river. Forefathers, gods, they worshiped and the land beyond the river. I mean, he's talking, being very intentional about their journey. And I'm sure the story must, they knew that, okay, hey, this is where our forefather Abraham built his first altar of worship as a response to God's promise. Right? The place, the first altar that Abraham builds in this land called Shechem is a very important one. That he wouldn't know that his descendants would eventually one day meet at the place and talk about everything that has happened in his own life. Right? I'm not sure if that's interesting or beautiful to you, but it's just so beautiful. Right? But anyways, let's just move on to verse eight, Genesis chapter 12 verse eight. That's where he builds the second altar. I'd like to call this the altar of intimacy and of the pilgrim walk. Right? So Genesis 12 eight says, and he moved from there to the mountain east of Bethel and he pitched his tent with Bethel on the western and I on the east. There he built an altar to the Lord and called on the name of the Lord. Right? He just built another altar. So if you look at the map, he comes down from Shechem to Bethel. And there he builds another altar. Okay. Now this was an altar of increased familiarity with this God that he's that he's been listening to that he's been obeying. And then he's growing in intimacy. This Abraham's walk is so symbolic of our walk of faith as Christians, isn't it? That as we walk day after day, after day, after day with him, as we, as we choose to obey his voice, as we choose to obey the leading of his voice, as we choose to trust our God. And then the more he responds, what happens? We grow in our faith, isn't it? We grow in our intimacy. Right? And if you look at the journey of Abraham from where he left, and he's come a long way, we can say metaphorically in his walk with God, that he builds his first altar, then he builds his second altar, the altar of increased familiarity and intimacy. Right? He was living a life of pilgrim. And this kind of this altar is corresponding to the verse in Hebrews chapter 11 verse nine. It says, And even when he reached the land, God promised him, that is the land of Shechem. He lived there by faith, for he was like a foreigner living in tents. And so did Isaac and Jacob, who inherited the same promise. I just want to pause here at this, at this point before we take our break. Is that one thing that we get, you know, we can learn is that as we walk and as we walk and journey through life, we can never become over familiar with this God, but we can only increase enough familiarity and intimacy. That's that's the key there. And another gentle reminder is that, Hey, we are also pilgrims in this world. We are just passing through like the famous books that says pilgrims progress. Right. It's just a beautiful reminder for us is that an encourage ourselves just like Abraham did is that we are also passing through this world. This is not our home. Our home is with the Lord. Yeah. I hope you're still with me. I'm going to stop the recording now for this session. We'll take a break and we'll resume next session in 10 minutes. Okay.


Hello everyone, this is Alice Gao. In this video, I will discuss the derivations for the smoothing formulas. The derivations for the smoothing formulas look even longer than those for the filtering formulas. Here's the first part and here's the second part. Don't worry about understanding all the formulas now. I will explain the derivation step-by-step. However, once we break it down and look at it step-by-step, you will see that each step can be justified by one of the five reasons that I discussed previously. For each step, please try to choose a justification yourself first. You will have five options as before. Base rule, rewriting the expression, the chain rule or the product rule, the Markov assumption and the sum rule. Let's look at the first part. In these steps, we wrote the probability as a normalized product of two messages, the first one from forward recursion and the second one from backward recursion. Step one, pause the video and choose an answer. Then keep watching. The correct answer is B, rewriting the expression. We split the sequence of observations into two parts. The second term contains the observations from the start to K to day K. The first term contains the observations from day K plus 1 to the end. If you imagine that you're in day K right now, then the two sequences correspond to past observations from the start up to yesterday, which was day K, and future observations from day K plus 1 to the end. Step two, pause the video and choose an answer. Then keep watching. The correct answer is A, base rule. It's easier to see this when you cross out the last variable in every term, O sub 0 to K, since it appears in all three terms. We switch the places of S sub K and O sub K plus 1 to T minus 1 using base rule. This is convenient since the observation sequence comes after the state on day K. It's natural to think about how the state on day K affects the observations in its future from day K plus 1 to the end. By the way, crossing out the last term doesn't mean that we can cancel it. I want you to disregard the last term so that it's easier to see the pattern in the remaining parts. This step is a version of the base rule where every term conditions on the same term. Here's a practice problem for you. Try proving the general equation yourself. You should be able to prove it with the basic rules of probability. Step three, pause the video and choose an answer. Then keep watching. The correct answer is D, the Markov assumption. This step removes O sub 0 to K from the second term. The Markov assumption is basically a conditional independence relationship. In this case, given S sub K, the state on day K, the future observations are independent of the past observations. That is, any observation up to day K is independent of any other observation from day K plus 1 onward, given the state S sub K. You can verify this relationship by applying D separation on the Bayesian network. Suppose that we're in day K right now. The path between any past observation and any future observation must go through S sub K. If we're considering O sub K, then the two red arrows are both pointing away from S sub K. If we're considering any past observation, the two orange arrows are pointing in the same direction. Either way, if we observe S sub K, it is as if we're cutting the chain at S sub K, making any past observation independent of any future observation. Let's look at the second part of the derivations. In these steps, we derive the recursive formula for backward recursion. We're going backward in time, given the probability of an observation sequence starting on day K plus 2. We can calculate the probability of an observation sequence starting on day K plus 1. Step 1, pause the video and choose an answer. Then keep watching. The correct answer is E, the sum rule. We use the sum rule to introduce the state on day K plus 1, S sub K plus 1. Introducing S sub K plus 1 is convenient, since it is a bridge between the state on day K or S sub K and the observations from day K plus 1 onward. Step 2, pause the video and choose an answer. Then keep watching. The correct answer is C, the chain rule or the product rule. This is easier to see if we cross out the last variable S sub K in every term. We use the product rule to write the probability as a product of two probabilities. Step 3, pause the video and choose an answer. Then keep watching. The correct answer is D, the Markov assumption. This step removes the value S sub K from the first term. This is another conditional independence relationship. Given the state on day K plus 1, S sub K plus 1, all the future observations are independent of the past state on day K, S sub K. You can verify this by applying the separation on the Bayesian network. The path between S sub K and any future observation has to go through S sub K plus 1. Whether we are considering the observation on day K plus 1 or any observation after that, the two arrows both point in the same direction. Therefore, if we observe S sub K plus 1, it is as if we cut the chain at S sub K plus 1, making the state on day K, S sub K, independent of any future observation. Step 4, pause the video and choose an answer. Then keep watching. The correct answer is B, rewriting the expression. We split the sequence of observations from day K plus 1 to the end into two parts. The first term contains the observation on day K plus 1 only. The second term contains the observations from day K plus 2 to the end. Step 5, this is our final step. Pause the video and choose an answer. Then keep watching. The correct answer is D, the Markov assumption. This is another conditional independence relationship. Given the state on day K plus 1, S sub K plus 1, the observation on day K plus 1, O sub K plus 1, is independent of all those future observations from day K plus 2 to the end. You can verify this by applying this operation on the Bayesian network. The path between O sub K plus 1 and any future observation has to go through S sub K plus 1. The two arrows are pointing away from S sub K plus 1. If we observe S sub K plus 1, it is as if we cut the chain at this state, making the observations on day K plus 1, O sub K plus 1, independent of any future observation. That's everything on the derivations of the smoothing formulas. Congratulations on making it through this video. If you will do one thing other than work or study this coming weekend, what would you do? Please post your plan in the week 8 post. That's everything for this video. Let me summarize. After watching this video, you should be able to describe the justification for every step of the derivation of the smoothing formulas. Thank you very much for watching. I will see you in the next video. Bye for now.


Hello everyone Welcome to another Narc survival live video as you can see I'm just messing around on the swings It's about 9 p.m. At night here just having a bit of fun Playing around got so much energy Gotta burn it off somehow So I like to come out and do this maybe not a good idea to do this one Must fell off but yes, and this one we're going to be talking about when the narcissist Turns everyone against you because yes, this is what they do When they fear that you are going to Reject or abandon them They fear that you may threaten to expose them Or maybe you have already questioned or confronted them When you do these types of things yes, they are very afraid Because they already know that they are hiding something They already know that they are doing something that is not right They're manipulating and abusing you They deceived you they lied to you the future faked They did all of these things wrong to you and they knew They did not have good intentions behind that They know that they didn't have your best interest in mind. They did not mean well for you And of course as I've said before The narcissist is always going to choose their false character of the illusion Over any source of supply Doesn't matter if you were their business partner, maybe you were in a relationship with them Maybe you were a family member a friend Whoever you were it does not matter The effect is still the same And yes the effect is that They will abandon you first They will try to control you. They will try to stop you from leaving They will try to isolate you. They will start a smear campaign against you They will try to turn everyone against you I think there's a frog here We're toad. Wow, it's cool to see that As you know, I just love nature. I love animals It's very still like a statue It looks like a toy frog But it is actually real But yes back to this message They will try to turn everyone against you They're very egotistical They have this exaggerated sense of their own self-importance and abilities And Yeah, just like they manipulated you And they got you to stick around all of that time all of those years Well, they never actually did anything for you. They just wasted your time Maybe your money and resources as well And then they go They manipulate up just as they did to you They get everyone To see you in the exact same way They try to control you. They isolate you And it's the same thing as they did to you They manipulate, they lighted them And in a way they also give them a form of future faking as well Well, yes, they may bring up the past They may turn Mohals into mountains And exaggerate all of these things that you are meant to have done in the past Or they just may make up things all together And it may not have any basis in reality But then they also future fake The enablers and flying monkeys as well But they're type of future faking for them. It's not that They're going to do or give something to them They future fake in a way where they label you as bad crazy or wrong And that is at some point in the future You're going to be up to something You're going to be doing something wrong Because you're this bad person, you're crazy, you're dangerous And of course I'm not saying that I just know that that's what they're thinking, the narcissist And that's what they've got in all of their flying monkeys to believe as well And Although I am in quite a good mood Right now I don't want to take the seriousness away From these situations I mean Clearly yes, I am someone that you can talk to, someone who will understand All of these types of things But the flying monkeys Even the enablers They are not the type of people that you can go and talk to And try to explain your side It's not going to work that way The narcissist already got to them, they beat you to the punch They got there first, they already manipulated them They got inside their heads And I know these things, these smear campaigns, the gang stalking It's a psychological phenomenon Or at least it's supposed to be Until you do enough research and you really understand it Because you've got to look at it like this That same narcissist who manipulated All of these people to turn against you Is it really that hard for you to believe? Because just look back That same narcissist manipulated you They made you believe in all of these lies and illusions all of that time And I don't know if you were with them for a few years Maybe a few decades All of that time they had you caught up They had you believing all of these things And people may have came to you during that time and tried to tell you That you were being cheated, you were being manipulated And you didn't want to believe it And yes I know in time maybe you found my videos and you started to wake up But it may be different for you, you may be an empath You may be more able to understand these types of things As I've said before a lot of the enablers and flying monkeys They are in fact narcissists, borderline sociopaths, psychopaths as well So they're not going to come to that same conclusion as you did They could be around for 10, 20 years For the rest of their lives and they will never get it And yes I can understand that may be hard to believe Because although it may have taken you some time to figure it out You got it in the end But it's not going to be that same way for them Because a lot of you because of your empathy You pull out of it because you want to be of service to someone You want to help people Narcissists are not thinking that way They are in it for themselves To get supply And they see you as the perfect target You've already been manipulated You've already been groomed by the narcissist So they haven't even got to do any of the work It's already done for them It's the perfect set up for all of these predators to come in To swoop in and take you out Or keep you down rather So that is typically how that happens But just why yes I can tell you that you are wasting your time Trying to get them to understand Trying to get them to believe you Doing that you're just going to waste your own energy It's just going to drain you It's going to confuse you Because as I said a lot of them already know exactly what they're doing They may already know that there's nothing wrong with you at all But they love the reactions you're giving to them You believe what they're saying You're listening to them You're believing that there's something wrong with you And you're trying to defend yourself You're trying to prove something to them And they love it when you're doing all of that But you need to stop trying to convince them I have been a victim, a target of multiple sphere campaigns throughout my entire life And one thing that I've learned Is that there is no point explaining or justifying yourself To people who don't even care They honestly couldn't care less If there was something wrong with you or not If you did something wrong or not They don't even care about that They just use it as an excuse Because everyone knows Or should know That there is no excuse for abuse And I hope that you will know that as well If you are one of my subscribers If you watch my videos You should not go around Exposing people To the public And yes I understand it's sad that the reason why these narcissists do this a lot of times Is because they were scared, they were afraid That you were going to expose them And that is why a lot of times they expose you And I don't know about you But in my situations What I became the target of sphere campaigns I actually never intended to expose anyone I was never thinking of doing that at all Yes I may have confronted the narcissist Or people who knew them People who were close to them But that was never my intention at all to expose them Because I am actually a very loyal and devoted person And that completely goes against what I believe in I already know that would make me wrong To make something public About my relationship, my family To put their names out there I already know that that would be wrong of me And I don't advise any of you to do that as well Because I personally believe that that is wrong But yes these narcissists that is what they will do They will blame you and they will tell everyone about it Because if you haven't figured it out by now They are not loyal Plane flying above I'm going to be on a plane now in a couple of days flying out But yes they are not loyal And the crazy thing about it is All of these enablers, these flying monkeys And you may have been an enabler or a flying monkey for the narcissist as well At one point All of them they think are Yes we have the sense of loyalty, the sense of belonging to the group To the narcissist Or to the other flying monkeys and enablers But that's exactly what you had as well And you may have been the closest person to them And they still got rid of you You may have been the most loyal person they ever had in their lives So it really just shows you how delusional All of these flying monkeys and enablers really are If you devoted all of that time, energy, money and resources to the narcissist And they got rid of you It just shows that they really are playing everyone for a fool And yet you were the one you probably cared more about them Than anyone else did in their entire lives And they got rid of you And now they're surrounded by all of these fake people who probably don't even care about them And they're all just using each other And yet you're worried Maybe you're angry, you're upset That the narcissist turned these people against you As I said I don't want to take away the seriousness from this From this situation But when you look at it, it's like who cares When you look back and you realize that you were the most loyal devoted person to them You cared more about them than anyone else in their lives And they got rid of you Why? Because you did one thing wrong If that's all that it takes To be thrown out of a business partnership If that's all that it takes that you do One thing wrong And it's not even a big thing Maybe you didn't even cheat on them You didn't lie to them You didn't steal from them You didn't do any of those things And yet that's all that it takes For them to get rid of you Then why would you want to be a part Of something like that to begin with Because clearly there is no place for someone like you in that You're far greater than that And they already knew it That's why they turned everyone against you Because they already knew that you were going to shine the light on them And everything that they did to you They abused you, they manipulated you, they tricked you And I know they did that Because that's how you found my videos in the first place You wouldn't have found my videos if you didn't think that you got cheated You got robbed You wouldn't have found my videos if you didn't think that So I already know And I am not the type of person To fall for these tricks, these childish games No one is going to come on here And make me turn against anyone I'm not going to give anyone advice Even if you are dealing with a narcissist I'm not going to be your flying monkey, your enabler I'm not going to team up with you to tear anyone down If you expose them to the world No, we do not do things like that on here We promote good righteous behavior And I recommend for you to do that as well There needs to be a distinct line between you and them Something that separates you Because there is clearly a difference of character between you and them They're going out And they're doing all of these things to tear you down When that is something that you never would have done to begin with You never would have engaged in that type of behavior But guess what, they're so afraid, they're so scared They may have thought you were going to do that They may have thought that you were going to reject or abandon them Even after your years of loyalty and dedication towards them They thought you were just going to toss them aside and forget about them And the reason why is because they don't even know you All they know is that that is exactly what they were about to do to you That is what they did to you So take a good look at yourself And realize how much of a better person you are than them Because I believe that these traits, I mean for me Loyalty is number one There is nothing more important than that to me And of course that is how I'm able to get on you every day And make these videos Because yes, I am loyal to you And I've always been loyal to everyone in my entire life At least until they abuse me Until they put their hands on me without my consent against my will Or maybe they mentally raped me I don't condone loyalty in those types of situations Nala's trying to get out of the car Nala's going to leave now I'm going to see her for a while I'm flying out in a couple of days Going to miss her a lot But we have been separated many times in the past Again, it's loyalty Even my cat I am very loyal to my cat Don't know if you know but I had her when she was eight weeks old She's six years old She's still very happy, very healthy Spent so much money Flying her around Paying for pets it is Maybe tens of thousands of pounds Over the last few years But it's worth it for my cat And do anything for my cat And do have a daughter as well It was a bad situation, it didn't end too well I haven't really talked about it much But I haven't seen her for a couple of years And my daughter, I would do anything for her as well Because for me Loyalty is not a family Family is everything But at least until they turn their backs on you When they start to turn people against you They start these campaigns But that is not right And I don't care if it's your own family Someone you're married to It's wrong And you need to recognize that And separate yourself from it I mean many of you, you're so caught up in it You're listening to what they're saying about you You're looking at yourself Thinking that something is wrong with you To the point where you're not even looking at everything they're doing to you I mean at some point you've got to be like Forget about whatever it is that I'm meant to have done What about what they're doing to me And maybe you're trying to make a change Maybe you're trying to be better I mean that's why you Likely confronted them Questioned them Because all you really wanted is for them to treat you better Maybe you just wanted a more functional situation And then they took that as abandonment It was though you were going to expose them When all you really wanted was some space, some peace Just some time to be alone You just wanted to work together with them to make things better Yes, because they're so hypersensitive to rejection They just went all out and tried to turn everyone against you A lot of times that's what they do, they get us completely wrong And that's just how it goes a lot of times But yes, I've got to go It is getting quite late I've got to check in at another condo now tonight I do hope this message was helpful I know a lot of you out there are going through this And as always, I will talk to you in another video very soon


But do you, don't you be surprised if I'm not here when you look behind? Guess I have my own destination, and you're staring at the wrong direction. I'm not looking for your confirmation. Good morning, my beautiful internet friends. You will never guess what we're gonna do today. Or at least I would never guess what we're gonna do today. We're going to a Ninja Warrior gym. I don't actually technically know what to call it. It's like, you know, American Ninja Warrior, where people do cool stuff. I'm gonna try to do that. I'm not sure how much of it I'm actually gonna be able to accomplish, as with most things so far, I'm suspecting it'll be more than I think. So let's go give this a shot. I have a buddy who works here and he invited me and I thought, what the heck, let's try it. How do you feel? Incompetent. We're gonna make this work. Don't be into my daytime. I am. You guys, I always have to do it. I can never do that even when I was a kid. Start there. I need more upper body strength for this. So far, so good. Okay, hand on both. There you go. There you go. All right, now it's all core, right here. It's all core. Put those feet up. That's it. That's it. You did it.  It's attacking me. That was awesome. Ninja gym day. I was able to do, then I actually thought I could. It's amazing. When I'm like doing sports or activities that don't actually make me focus on what I'm doing, how much I forget that like, it's just my leg now, which feels really good. A huge thank you to altitude ninja gym here in Colorado Springs for having me. That was a riot. Also, I'm super out of breath and my arms are shaking and I have no muscles after a year and a half of doing nothing. Since most of us are adults, we're aware of the fact that our actions have consequences, right? Well, yesterday's actions had consequences. First of all, it was absolutely amazing. I'm still kind of feeling a high from being able to do the things I was able to do. And I was looking over some of the footage and it was like, oh, I actually did those things. And that was really cool. But the rest of the day, after I got home, I wasn't able to wear my leg at all. I think I really accidentally pushed myself too far. Like in the moment, I wasn't like, I'm going to push through this pain. But when I got home, I took my leg off for like an hour and then there were still red marks on it. And that's when you should not, you shouldn't keep wearing your leg after that point because if there's red marks lasting longer than 15 minutes, that's not super cool.  And oh my Lord, I woke up this morning to so much soreness throughout my entire body. Like my shoulders and my little biceps and my abdomen. I giggled at a joke earlier and paid for it. It feels really good to physically be sore from something that I chose to do. So that's happy. But also, man, I've got a long way to go. This has been very inspiring to me to keep pushing myself in a healthy way and, you know, making sure I don't injure myself or anything like that and stopping when I need to. But I can do so much more than I think I can. It made me start thinking about like the 5K that I'm training for, right? I wonder how far I can actually walk without being in pain. I may actually try to give that a shot later and see like, what is the longest that I can go on a fairly even surface without damaging my leg or hurting? If you guys have been interested in seeing that video, let me know. I may try that this weekend when I have some time. But thanks for listening. Thanks for coming on this journey with me. This was so much fun to do. If you are in town or in Colorado or ever come visiting, please go check out Altitude Ninja Gym. It was a blast. They have really cool equipment there and are super nice people. So I appreciate them having me. Thank you to my patrons who make these videos possible. I appreciate you guys more than you know. Sincerely, thank you. Yep, the neighbor dogs are barking. It's time for me to go. Hi, Mikey. Puppy. Oh, hi, Sophie. You got everybody. I love you guys. I'm thinking about you and I'll see you in the next video. Bye, guys.