Hello and welcome to NewsClick. Today we have with us Prof. Ajaz Ahmad and we will be discussing what is happening in Gaza. Ajaz, this fresh attacks on Gaza. How do you read it? Is it basically because of the impending elections in Israel or is it a deeper strategic issue that Israel is trying to resolve? Well, it's hard to read. At a certain level, it looks like the replay of 2008-2009 invasion of Gaza in which some 1400 Palestinians were killed, 5,000 injured and so on. It was a devastating attack. That came immediately after the U.S. elections, before the inauguration of the U.S. president and just a few months before the Israeli elections. That is exactly the scenario right now. Obama has been re-elected on the 6th and this began on the 8th. They are probably going to wind it up before 20th of January when it starts the second time. The timing is eerily like that invasion. The operation cast lead of 2008-2009, December-January that year. Number of people including the chief of the army staff in Israel have been bragging for an attack. They are saying that we have to neutralize this new capacity of the missiles in Gaza and so on and so forth. So they have been building up towards this and it sort of appears as if they were just waiting for Obama to get over his election campaign and do it. It all appears as if they are all set for a whole big invasion, a repeat of that kind of invasion of Gaza. The Israelis seem to be. Just last time, their supposed goal which is to take out Hamas militarily did not succeed. In fact, Hamas capacity to retaliate still continues. This time, why does Israel think it will be different? Eventually what they achieved at that time could have been achieved without that level of massacre.  You will recall that most of the bombings took place in the north where there were no such missile batteries or anything of that sort, not closer to Israel. There is a view that the idea was to terrorize the population and make it flee, which has been one of the objectives of the Israelis. To achieve what they set out to achieve last time and fail to achieve, now they wish to achieve, to really achieve it, they'll have to reoccupy Gaza altogether. Short of that they cannot do it. Now what you have is that the missiles are not or rockets are not controlled by Hamas alone. Islamic jihad seems to have more sophisticated, I mean quite sophisticated missiles now in fact, one of the rockets that fell outside Tel Aviv. Islamic jihad says that it was theirs and they say it was Fajr 5 which Iranis have given them. That is what they say. There are other jihadi groups not controlled by Hamas who are rising, saying Hamas is colluding too much, Hamas is making peace with Israel and so on. These long term ceasefires that they are constantly negotiating and so on. Hamas has not delivered. You will recall that Hamas grew so much because the Palestinian Authority did not deliver. Now the same discourse is happening in Gaza with these smaller groups. So if you now delegitimize Hamas any further, you may not achieve what is said to be the objective but you may achieve two other objectives. One, you weaken the Hamas thereby you strengthen relatively these other jihadi groups which are under control of nobody. I mean they may be under the control of the Qatari or somebody but they are not part of that process of negotiations with Israel. And secondly one thing that is being talked about, about which there isn't much evidence to my knowledge is that there are growing fissures between the leadership of Hamas that is inside Gaza and the leadership the Politburo members who are spread across the Arab capitals and now primarily in Doha. That between the external and internal which is a classic situation of conflict, it is said that Jabari was part of Amr Jabari too which will come in a moment. Who is the head of the military wing of the Al-Qassam Brigades of Hamas was part of that conflict representing more than internal forces as against the external forces which are much more and the external forces are said to be much more in conversation with Arab governments particularly after Hamas evacuated Syria and went on to primarily be in Doha although then spread in some other capitals as well. It might well be that that is one of the objectives. So there are sort of series of hidden objectives. If Israel cannot achieve its military objectives without full-scale occupation, reoccupation of Gaza at least for a period of time and if it does that then it has other consequences. What does Israel gain in the region? Because right now the situation is that the Islamicist governments of Qatar, of Egypt, of Turkey are all doing the dirty work of the Israelis in Syria. We'll just come to that in a moment. Let's go to the Gaza issue further. As you said Jabari assassination when particularly when there was already a ceasefire which had been negotiated by Egypt and there was also a proposal on the table for a long-term ceasefire with Israel which had been negotiated and Jabari was the man who was doing it and he received a full-fledged draft of it which had come from Israel approved from the Israeli side of his negotiators for presentation to the Hamas leadership just a few hours before he was assassinated. So as the person who was negotiating that ceasefire as said it's a pre-emptive strike against the ceasefire. So how does one read this? Does it mean that Israel needs war to continue at a low level in order to hold its population into the kind of genocidal policies it has adopted? Do you think that is its political requirement? I don't know. What is very eerie about this is and I have no evidence but I'm just wondering if the delivery of that to Jabari was not the point at which they found out where he was. That this was in fact itself a ploy to get him more and more exposed to the intelligence networks of Israel that Israel was never serious about it to start with about this long-term ceasefire. So it appears then that one target of course is the election in which now Avigarh Liberman and Netanyahu have combined to a very right wing I mean within Israel it's difficult to say who's more right wing but certainly this is the more fascistic this is the far right so the far right agenda and the far right agenda really needs a warlike situation all the time in order to rally its population behind it so that's again again I'm confused about that between the two of them they've really got the majority and the Labour Party is in such doldrums that as soon as they started Bombay Gaza their chief made two very significant statements in one he says that people make a mistake when they describe Labour as a party of the left we are not a party of the left and then he congratulated Netanyahu for finally taking the initiative that he needed to take to do all this in Gaza so he has lined up entirely with them and so has Khadima so has Khadima so I mean but but my sense is that Khadima and Labour were in such bad shape anyway that fusion of the two parties had already guaranteed the election for them anyway they didn't need it they didn't need it but you know I mean if you can win win by 60% why not win by 80% and do whatever you then intend to do so certainly certainly elections are certainly what I am talking to at this point and what I'm trying to think through is what is the would be the logic of a full scale full scale offensive of the type that took place in 2008-2009 now on Thursday alone they killed more Palestinians than the Palestinians have killed Israelis in 13 years since Wednesday there have been close to 300 aerial bombardments across Gaza how much more full scale invasion there will be you know is it that now it's perfectly possible that on Friday that is today the Egyptian delegation will come they will initiate the discussions for a ceasefire they will make speeches in the Arab League and Security Council and so on meanwhile Israel keeps bombing at this rate and a week from now there is a ceasefire for which Egypt is given the credit is that the game so it's it's very open just how far they intend to go the other thing I would like to bring up is this they thought that this iron iron dome the missile shield that they were building that will effect effectively protect them but 50 more than 50% of the rockets are actually gone through it does seem to indicate that this strategic idea that they can hold off take out Gaza militarily and protect themselves with this kind of shield is not really going to long run absolutely and there's that that's an excellent point beyond that the fact that a rocket that has come from Gaza has fallen so close to Tel Aviv virtually in its suburbs is a game changer because Tel Aviv bourgeoisie has felt so secure all this time and is having a hell of you know hell of a time completely indifferent to the Palestine issue as if it does not exist the fact that two such missiles actually fell in Tel Aviv shows that the the missile shield doesn't work and in fact these cities are more vulnerable than ever before and if that is the case then can they take on his bullet which is a far greater capacity far bigger arsenal far better arsenal far bigger arsenal for far better arsenal and far more seasoned personnel so you know so other things other other interesting point is that this ability of the Gaza militias Gaza militants to strike Israel as well as of course as Gullah is only going to go over to grow with time so effective striking power into Israel can only increase and not decrease so if they want peace the only way for them to get peace is actually to set a negotiate which is not willing to do and you see you see probably the way the media covers these things it is as if after 2008 2009 invasion this is the next one as if there have been four four four years in which Israel has not done anything Israel killed over a hundred people in 2011 in Palestine it injured around 500 people there have been you know 600 Palestinian casualties in 2011 alone so despite this constant bombings assassinations that and the other despite all the blockade they can't even get medicines you know they're heartbreaking stories I was reading Shomsky's piece he tells a heartbreak story about somebody dying because there was no medicine for cancer and yet their capacity rocket capacity has increased dramatically half of Israel is now effectively under the Israel rocket reach the main thing is if you can get to Tel Aviv that is true then it doesn't matter what you know rest of the other yes it is that you know I don't know 60 miles of 90 60 kilometers or 90 kilometers something like that that Tel Aviv is from the from the Gaza strip if you can endanger Tel Aviv and if the Tel Aviv middle classes and upper middle classes can wake up to their own vulnerability you have changed the terms of the game just two other points in what you've just said one is the fact that in the past almost all such temporary ceasefires have been broken by Israel is a study now it says that more than 90 percent of the attacks after in lull has been from the Israeli side yet the western media pretends as if it is always Israeli retaliation and it is always as if the Gaza have attacked I consider it as a complicity in war crimes I I really do it's not a rhetorical position I really do that this is a complicity in war crimes and this has been going on for decades now the second point is that you pointed a bit earlier that it's even this time there is an Israeli minister now who has said who should it attack in a way that the civilian population flees from Gaza so that could be of course a temporary agenda as well to make the people leave for Egypt but even if we think it's not a tenable one this is this is a permanent agenda you know this is a permanent agenda and you know that that is the agenda behind the starvation of you know this minimum nutrition availability per capital as if that minimum gets to everybody in Gaza in equal measure you know this sort of thing you know 400 trucks of truckloads of food used to come into Gaza before this blockade began in 2006 and now 6065 will be allowed that starvation is a constant pressure for people to flee this lack of medicine and so on sanctions and all that so that that is there and that is what I was saying that even now you see the same pattern in bombings that the bombings are all over Gaza from the into the areas that are farthest from from Israel and where there are no missile batteries so that is again terrorizing the population large right either you flee or you terrorize them in such a way that they're incapable of lifting their heads it's a certainly certainly master certainly master we'll come back for a second installment of this discussion be with us when we discuss the Gaza again


Hi, this video is called area of a regular polygon formula. So by the time this video is done, you will have developed a formula for area of a regular polygon and done your first example using the formula. This first slide is dedicated to helping you see where the formula comes from. Instead of just giving it to you and asking you to trust me, you'll actually be able to see its development. We are going to use this regular pentagon. So by regular, we know all five sides are the same. We're going to use it to help us find our formula for area of a regular polygon. So even though I'm using a pentagon in my example, this formula will hold up for any regular polygon. So any sort of a shape that has all congruent sides and all congruent angles. Alright, where to begin? I have my pentagon. I'm going to look at the shape underneath it. I've got a parallelogram up on the slide. You all have learned that area of a parallelogram is base times height, where the base and the height are perpendicular to each other. They meet at 90-degree angles. We're going to use that now to help us with our formula. So let's think about this. If I look at my pentagon for a minute, I've got one triangle sitting inside of it. I got that triangle by drawing in radii. Let's go ahead and draw in all five radii that a pentagon will have. And you can see that a pentagon that has five sides has been fairly easily broken into five congruent triangles. So why don't you go ahead and draw in the radii and then just kind of lightly shade in your five triangles. What I'm going to do is kind of pretend like I cut this pentagon into five triangles and see if I can fit it into the parallelogram below. So here we go. This is what's going to happen. I'm going to make my first triangle, move my first triangle down right here. I have four more to go. My second triangle, I'm going to put it right next to it. My third, my fourth, and my fifth. So what I've done is I've taken the five triangles that were in my pentagon and rearranged them so they're sitting nicely in that parallelogram. I did that because I know the formula for area of a parallelogram is base times height, so I'm going to use that to help me, okay? So let's look at this. In my parallelogram, how much of the parallelogram was filled up? I have one, two, three, four, five triangles that were filled up and one, two, three, four, five that were not. So if I know that the parallelogram is base times height, I think my pentagon will be base times height, but only half of that. So one half base times height, or you could say base times height, divide by two. Mathematically, it's more proper to follow the formula one half base times height, but base times height divide by two is the same thing because multiplying by one half and dividing by two are the same. So you can see that we find the area of our pentagon by finding the area of a parallelogram and either multiplying by one half or divide by two. But now here's the thing. I don't want to have to do that every time where I take my shape and see how it fits into a parallelogram. So let's change our formula, and instead of using it in terms of the parallelogram using the base and height, could I rewrite it a little bit so it's in terms of my pentagon? So let's think about this. So what I'm trying to do is instead of using b and h, I want to use letters that come from my pentagon picture to help me. So looking at this, instead of calling the height h, what could I call it? Well remember, if this is the base of my parallelogram, the height will be a distance that meets it at a 90-degree angle that's perpendicular. So this could be considered the height. This could be considered the height. This could be considered the height. This could be considered the height, and so could this. So instead of calling it h, let's call it a for that apathome or apathome. Okay? Now what could I rename the base? Well the base of my parallelogram was this entire bottom side, which looks like it was the bases of all five of my triangles. So if I go back up in the picture, the bases of all five of my triangles are the distance around. What else could you call that? Well, the bases of the parallelogram, being the bottom five bases of my triangle is actually the perimeter of my pentagon. So instead of calling it the base of the parallelogram, let's call it the perimeter of my pentagon. So my formula, my official formula for area of a regular polygon is one-half perimeter times apathome, where it's the perimeter of the pentagon and the apathome or the apathome of my shape. So we could say one-half p times a, or p times a divided by two. Remember both formulas are fine, but the one-half p times a is more mathematically proper. I personally don't care which one you use. Ask your teacher if they have an opinion. This is Mrs. Milton. So if you don't have Mrs. Milton, ask your teacher if they care which formula you use. All right, this video isn't quite done yet. Now that we have our formula made, let's just quickly go through one example so we can use the formula. When this video is done, you will be done with the front side of your note sheet. We are now in the block that says number two. Find the perimeter of the regular polygon. Well, this is just giving us a little bit of practice. If it's a regular polygon, that means all five of these sides are the same. Since one of them is marked with a six, they all will be the six. So what's the perimeter? You could say six plus six plus six plus six plus six, or you can say six times five. You're going to get a perimeter of 30 units. All right, let's go to the next slide. Again, we're just practicing little pieces and we're going to put it all together really soon. Number three on the front side says find the central angle or CA in the regular polygon. Well, remember the central angle goes from the center of your pentagon, I'm sorry, out to the vertex. So since a pentagon has five sides, we'll have five radii. So that will make five central angles that are all the same. Well, like we mentioned before, all those central angles should add up to 360. And if they're all the same, they're going to divide by five, and that gives us 72 degrees. So I know all five of these central angles are 72 degrees. Okay, again, just one piece to the puzzle. We're practicing all the different parts. We'll put it together soon. The next one, number one, or number four, it says find the length of the apathem or apathem in the regular pentagon. Well, I'm going to just catch the picture up a little bit. All of these central angles were 72 degrees. And remember how all of these sides were six. We talked about what the apathem or the apathem does to the side of your pentagon. When this apathem dropped down, it split that into two, so we really had three and three here. So now I've got to kind of think about what could I do to find that apathem? Well, remember, in my pentagon, I've got five triangles going, and that apathem in that bottom triangle, it cut my triangle in half into two separate triangles, and it made a 90-degree angle. So sure enough, we have got a right triangle. So I'm taking this guy right here and making him bigger. We have a right triangle where this bottom side length was three. Here's the apathem that I'm trying to find. And what happened to this central angle that was 72? Well, when you drop an apathem down and it cut the segment, it bisected the segment into three and three, it also bisected the angle. So the 72 got cut in half to create 36. So we also have two angles that are both 36 degrees. So up here, I've got a 36, I've got a 90, and then I would also have... this would end up being a 54 because 36 plus 90 plus 54 is what adds up to 180. So now, hopefully, where everything's been pretty new, this is starting to look familiar, that we actually have Sokotoa. It's not a 30, 60, 90. It's not a 45, 45, 90. So I'm going to use Sokotoa to figure out what this apathem length is. So let's try to remember, I'm going to go... you could go from the perspective of the 36 or the 54. I'm going to go from the 54. It makes the apathem my opposite and three my adjacent. Well, opposite over adjacent is a tangent. So I've got the tangent of 54 equals the opposite, which is A, for apathem over the adjacent, which is three. I'm going to put the tangent of 54 over one. I'm going to cross-multiply. A times one is A, the tangent of 54 times three. Well, the A is already alone, so all I have left is to multiply. When I multiply those, I get it to round to 4.1. So my apathem is 4.1. All right, so now it's time to put it all together. You can see on this last slide on the front page, I've got a picture of my pentagon with the side length of six. I just found that apathem length in my last slide to be 4.1. So let's find the area of the regular pentagon. So it's time to put it all together. My formula that I learned is one-half perimeter times apathem. So I need to replace the P with the number and the A with the number. I just got the apathem to be 4.1. And if you can remember, we've already gotten the perimeter to be 6 times 5, which was 30. So now it's just time to simplify. Since it's a multiplication, one-half times 30 times 4.1 can multiply it in whatever order I want. I'm just going to go left to right. One-half times 30, that's the same thing as 30 divided by 2 is 15. 15 times 4.1 gets me 61.5 units squared. So you have finally, in your longest video yet, just completed a problem to find the area of the regular pentagon. There's some things we're going to have to talk about with rounding. We'll deal with that in some later problems to really concentrate on that part. But for now, you've learned how to use one-half perimeter times apathem. You've just finished your first problem. Now it's time to do a lot more so you can get good at this.


All right, I think it's time that we start our third session. Yes, I'm Lasmus Bult and I'm super happy that we have Richard McElrath with us today. I first encountered Richard McElrath's name when I found Brad who is a book in one of my colleagues' books case and I thought it was great. And now, a couple of years later, I just checked, your book is the second best celebration statistics book on Amazon. Just second to government's station data analysis, which is amazing. So I'm super happy that you're here. Welcome, big applause. Thank you, Lasmus. So I'm very happy to be here. This is my favorite kind of conference, because it's cozy. So in thinking about the kind of talk to give, I thought most of the talks would be a bit technical, so I decided to give a fairly non-technical talk aimed at kind of a confluence of my interest in Bayesian statistics. And so let me give you some background. I'm not really a statistician, at least not originally. I'm an anthropologist and I come to statistics with a very definite topical interest. I study human evolution and in particular the evolution of human behavior. And one of the methods we use in anthropology to study that is ethnography. And the ethnographic method to the extent that it has one at all is that you go places and you live with people so that you can get an inside view of their society and how it works. So you want that inside view because it helps you develop a better outside scientific understanding of variation among societies. And so this is me during my PhD work. I spent a couple of years in Tanzania getting an inside view of culture there. When I came to study statistics, I applied the same ethnographic method to learning Bayesian statistics. Take the inside view and I got that perspective from some of the famous writers in the field. My commitment to Bayesian statistics grew out of the strengths I found in that inside perspective. It makes particular things easy. And it fits in particular with the kinds of difficulties of the data we collect in anthropology. And so what I want to do today is use this as a launching off point to talk about what I think is there are systematic problems in teaching Bayesian statistics because most people encounter another paradigm first. And then there are top Bayesian statistics from the outside view rather than the inside view. And so I think we've got a lot of work to do as a Bayesian community in better developing an inside view that we can agree upon because I don't think there is one actually. So I'd like to start this conversation by proposing some elements of an inside view and illustrating them in the sense that they provide pragmatic solutions to common data modeling problems of at least the kind that I study. So first, a little bit about what the outside view is. The outside view is fine. I'm not going to say bad things about it. It's just the outside view, at least not today. So this is the honorable Sir Ronald Fisher, who certainly not the only person associated with the outside view but he defines likelihood in the way that most people use the term likelihood. And maybe you've all read this by the time it's been up here on the slide for a little while already. You don't need to read it all just to say that likelihood is defined in a very odd way in statistics. It means a very special thing. It's a function. It's not a probability. It's a function of parameters. It's not actually conditioned on the data. There's a semicolon thing because you can't marginalize over it. Weird stuff like that. And that's all fine within that paradigm. But then when people encounter Bayesian statistics, they are taught that we use this likelihood and then we add priors to it. And then now you're Bayesian. And that is incorrect, of course. And I think there's mental friction that's created from that. So very quickly, the outside view has a bunch of elements. And the outside view is actually a lot of different views. But some of the common elements that people come across before they learn Bayesian statistics include things like the data head distributions, the parameters don't. There's a very important distinction between parameters and statistics, at least in the Fisherian view. The likelihood is not a probability distribution. I remember being screamed at for calling it a probability once in a math stats class. And there's this imaginary population that is a device for creating uncertainty in statistics. Now, this is the frequentist sampling theory view. And then, after you've learned all this and passed some exams on it, you learn that Bayes is all this stuff, plus we add some priors. This lets us do Bayesian updating. And these priors, well, they're very subjective sort of problem. I'm not going to spend any time arguing against this outside view. Although, if you judge from this art I have on the slide, you might get some idea of how I feel about it. So let's say that the outside view teaching Bayesian statistics is like the British going to Egypt. They disrupt the society quite severely. It's a colonial view on the statistical paradigm. And therefore, it's a failure to take the inside view. And so it gives up some of the strengths of the perspective. And the full strength of the Bayesian perspective is unleashed by taking some insider view of what goes on. Not deriving it as sampling theory plus priors, but rather taking it on more fundamental terms. Of course, I'm not the first person to say this. Dennis Lindley put this in probably every one of his papers, a complaint of this kind. So here's probably the most succinct quotation from him. He says, what most statisticians have is a parody of the Bayesian argument, a simplistic view that just adds a woolly prior to the sampling theory, paraphernalia. They look at the parody, see how absurd it is, and thus dismiss the coherent approach as well. Lindley has some very colorful papers, by the way, if you've never looked through them.  So the conceptual friction in my experience teaching statistics that arises from the outside view plus priors, rather than an inside view on Bayesian inference, include things like students coming to believe that the data must look like the likelihood function, or at least that the residuals need to look like the likelihood function. The outside view, maybe that's true. On the inside view, it's definitely not true. This concept of degrees of freedom is something people are taught in an introductory stats course, and then they encounter Bayesian models where you have like a thousand parameters and ten data points, and they say, you can't fit that, and I say, watch me. Now, it's not that you're going to get much updating from that, but you can definitely fit it.  We use those words to describe Bayesian models. We cause problems with the understanding among our students and ourselves. Sampling is a source of uncertainty. It's true in non-Bayesian approaches. Definitely not true in the Bayesian approach. You can have uncertainty that isn't stochastic at all, purely epistemic. Defining random effects via the sampling design, I'll have a little bit more to say about this later in the talk. And often, although it's not a necessary feature of the outside view as I'm calling it, a neglect of data uncertainty. When there's measurement error, people wave their hands a bit and say, yeah, I worry about that, and then they fit a model that ignores it. And in the insider view, I'm going to try to convince you there are obvious solutions to common problems like uncertainty and measurement. And all of you probably have your own conceptual confusions that you first encountered when you started learning Bayesian statistics. So now I have to admit my book perpetuates this problem. So I just started trying to do the second edition of this now, hacking away at bits of it. And I had to fully engage with my guilt over the problem that I feel bad about many of the choices in the book, as all authors do. And foremost among those regrets is that it uses the outsider vocabulary. I use terms like likelihood and parameter and estimate in ways that really only have coherent definitions outside of Bayes. And people tell me they learn things from my book, so I guess it's not awful, but I think we can do better. I think I can do better on a second pass. And I want to start thinking about that in this talk. So one of the problems is that this generates friction because using my colonialist metaphor, this is like explaining Indian politics using British political parties. Well, there are these things called casts and there's the Hindu system and all this other stuff that matters, and none of that exists in Hogwarts or whatever. So inevitably there are things that just cannot be explained in terms of the other framework. When this perpetuates lasting confusion, people thinking, for example, that tilde means sample. Who was I talking about this with recently? Yeah, with Rasmus. We may ask perhaps that this is a historical necessity to use terms like likelihood because people still encounter non-Bayes statistics first, but I'm at least willing to try with all of you to do better. So let me try to outline another path in the remainder of my time today. The claim I want to entertain, I'm not sure I'm convinced myself of this yet, is that Bayes is easier and more powerful when we understand it from the insider perspective. Now the key problem first of all with this claim is that there are lots of insider views on Bayes, right? Bayesians argue amongst themselves as well. This is classic paper 1971 by I.J. Good called 46,656 varieties of Bayesians. Anyone else know this paper? It's a two-page paper. He's thinking he has 11 criteria and he goes through the permutations of all the combinations of them and it's actually, it's a really nice, you can learn a lot about the epistemic possibilities from this. Yeah. I had artificially made some facets discreet. My heading would have been on the infinite variety of Bayesians. So I'm going to pick a particular insider view that is useful to me and solve some particular problems, but I don't think it's unique in being an insider view on Bayesian statistics. So here's the insider perspective that I use most of the time. The key thing about the Bayesian approach that engages me as a scientist is that it's a joint generative model of all the variables. What do I mean by variables? I mean data and parameters, because they're the same kind of thing in Bayesian statistics. This perspective has these two key unifying ideas that where things that are distinct and must be treated differently in the outsider view are indistinct and treated the same much of the time in the insider view. So variables, what we usually call data and parameters in the Bayesian view, in the Bayesian view data parameters are fundamentally the same thing. They're just variables. And sometimes we get to observe them and sometimes we don't. But they have distributions that calculations are done the same on and so on. Distributions likewise, there's no fundamental distinction between likelihoods and priors as there is in the outside view. I want to again say that there's nothing necessarily wrong with Fisher's definition of likelihood, that's the outside view and this is the inside view of it. So I want to give you some examples to try and back this up and give you an intuition about why I think breaking down these distinctions can be useful. And then hopefully we can have some conversations about exactly what terms we might want to use to refine this. So here's a kind of typical line from a statistical model, a mathematical statistical model. And I've used some Nordic runes in honor of the workshop instead of Roman or Greek characters to obscure whatever convention you would normally use to decide whether something was data or parameter. You probably don't have stereotypes about whether a futark rune is a parameter or data. So something till the normal something something. And so now I might ask you, is the symbol on the far left data, is it something that was measured? Is this a likelihood in that case? Or is it instead a parameter, which would imply it's a prior? And you can't tell, right? There's absolutely nothing about this statement which reveals which of those two cases it is. And that's because in a Bayesian model, it's the same kind of epistemic statement. They're fundamentally the same issue. And in for a common data generating model, a joint model of data and parameters, from one stage to the next, B might be observed, or it might not be observed. When it's observed, we treat it as data, we call that as a likelihood. When it's not observed, we treat it as a parameter, and we call it a prior. But it's the same statement about the underlying science. Does that make some sense? So I want to show you three kinds of models today, which are simple toy examples, but they're real working statistical models where this collapsing of definitions between data, parameters, likelihoods and priors is revealing of some of the unity of the Bayesian approach and why it behaves the way it does. So I think the cases I'm using are not necessarily the most common kinds of statistical modeling problems. People come across, say, in experimental sciences, and the experimental sciences, you're lucky to have clean data. You can set up your factorial experiment and fill all your cells, recruit more students, make it work, grow more yeast, whatever it is you need to do. And I'm an anthropologist, and in anthropology we go to war with the data we have, not the data we wish we had. So we deal with lots of inconvenient sorts of models, and I'm going to show you those. You might think of these as corner cases in your fields, and that's fine. In these corner cases, the distinction between data and parameters is often very hard to make. So this will include things like generalized linear mixed models, missing data models, and measurement error models. There are many, many kinds of strange machines, like occupancy models, joint species distribution models, have features like this, that have these features as well. Okay, so let me introduce the toy example, and then I'll go through three kinds of varieties of this toy example. In which this collapsing of definitions can teach something useful, if you're just learning Bayesian statistics, or maybe if you've even practiced it for a long time. So let's imagine a simple kind of observational experiment. There's a room in which there's a bird, and a cat. And the bird likes to sing, and when the cat is present, it scares the bird a bit, and it tends to sing less. When the cat is absent, or sleeping, say, the bird tends to sing more. There are four variables in this study that we're interested in, because we're estimating the rates, the effect of the cat in psychology terms. What's the effect of the cat on the bird singing? And so there are four variables. There are the count of notes in some interval. There's the presence and absence of the cat, right? And then there are these two unobserved variables, that are rates, which are calculated from these things. The rate of singing when the cat is present, and the rate of singing when the cat is absent. I hope there are people here who like cats. That's why I chose cats, because people tend to like cats, right? Put cats on slides. So just to summarize, we have two of these variables are observed, and two of them are unobserved in this simplest model. So you would call it typically the ones on the left data, the ones on the right parameters. As we move through examples, I would like to make you question those distinctions a bit. But for the sake of it, let's start with the initial joint model of these four variables. Again, the thing about the Bayesian insider view to me is that the model is a joint probability distribution for all the variables, all of them. And so what does it mean? It means this thing. I should have just put a P there. We were talking at lunch about how in statistics it's frustrating every function is called P. So you get P, notes, cat, rate conditional on cat, rate conditional on no cat. And I don't know about you, but I have a problem visualizing a four-dimensional probability distribution. So I struggled to try and put one on a slide, and it didn't come up with anything that looked great. So I'm just going to skip straight to saying, how would we define this in a conventional statistical framework? Here's a simple version that we can start working with, just to think about. The notes at time t are distributed as a Poisson variable with a rate lambda t.  There are two rates, alpha and beta. One for when the cat is absent, that's alpha, and one for when the cat is present, beta. And then, so we've got our two observed variables, notes and cat in here. You see how they're data, and they're affecting the rate. And now we've got our two unobserved things, and we need priors for them. We have to say what the distributions of these things are, unconditional on the data before we see it. And I'm going to assert these for the moment, and I'll justify them in a couple slides, that they are exponential with a mean of 10. Okay, with me so far? I'm assuming, and I apologize if it's not true, that everybody's reasonably familiar with this way of writing stats models. If not, you'll become familiar with it, and you'll learn to love it. It's like this is phrase Stockholm syndrome, right? It seems appropriate. Okay, Lund syndrome. So, how is prior formed? You might ask on the internet. That's someone who understood that joke. So, there are many ways that basings go about forming priors. I tend to come from a school where we don't talk about beliefs ever. In fact, it's almost like a taboo in anthropology to talk about anybody's beliefs. But we talk about other things. So, you can ask, what predata information do you have about the unobserved variables in this case? And so, let me walk you through what I think of as the worst case scenario for determining priors, and this is leading up to a pivot, so bear with me for a second. So, what do we know about these parameters before we've got any data with which to inform them? Well, we know that they're non-zero positive real values. Why? Because they're rates, and rates are by definition non-zero positive real values. You with me? So, that's gotta be true. And we assert that all we're interested in is the average. We want the expected rate when the cat is absent and when the cat is present. So, we're gonna track one thing about them. If those are the two things that we know prior to being able to get information about the rate, then there's this fun argument called maximum entropy, which gives you the most conservative distribution that embodies that information and no other information. And the solution to solving this maximum entropy problem is that you use an exponential distribution for the priors. You still have to pick that mean, so you need some information and additionally, but it leads inexorably to the exponential. You can use something else if you feel motivated to do so, but this is a maximally conservative approach that spreads probability as evenly as possible while being consistent with the things you've said. So, that's what we're missing. It's positive and it has a mean. Those are the two things. Then it's exponential. So, the fun thing about this argument, whether you like it for priors or not, is that this argument, when applied to likelihoods, gives you GLMs. This is the quickest and most conservative route to specifying all the families of likelihoods that Fisher would have fused and did use in his lifetime. The same argument. So, what do I mean? It's like if you know the metadata on the outcome variable, before you've seen the values and you apply the maximum entropy argument, you end up with the likelihood families, the exponential family likelihoods that you get. This doesn't mean you have to do it this way, but this is why I'm showing that in the Bayesian perspective, or at least in my Bayesian perspective, the way we derive likelihoods or choose them can be justified by exactly the same argument as picking priors from maximum entropy. And what that gives you is very conservative flat distributions, which blanket as much of the possibilities prior to data as possible. So, in this case then, like the priors, the likelihoods, these are pre-data distributions. Likelihoods don't tell you how the data have to look. They just give pre-data expectations about the blanket of possibilities that it will appear in. The data are free not to look like the likelihood because this is a prior distribution. The residuals don't have to look like that because you're going to update. Nobody thinks that the posterior has to look like the prior, but lots of people think that the residuals have to look like the likelihood, right? But it's not true. You will still estimate the mean, even if you use some other distribution, right? Now, p-values do depend upon the residuals having a shape, but the posterior being calibrated does not. So, in this case, we think about what do we know about the notes before we actually know the values? We know that they're zero or positive integers. It's a count variable. And we know that all we're going to keep track of is the expected value. Again, maximum entropy leads to a unique solution, and that's the Poisson distribution, which is the maximum entropy distribution in this case. So, again, if you have other information, you could put it in and end up with some other kind of likelihood, but this kind of argument gives you all the conventional likelihoods of non-Basian analysis as well. And these are maximally conservative distributions. So, the point of that is that there's a unity to interpretation and derivation of likelihoods and priors, even in the simplest kind of what we call regression model, generalized linear mixed model. There's not even any mix here, generalized linear model. And that unity of interpretation and construction is incredibly useful for heading off misunderstandings like thinking that the residuals have to look like the likelihood. Here's how you'd implement this model. Just to prep you, this is not a complicated model, but I'm going to have, for all the models in this, I'm going to show you a slide like this. I don't intend to walk through the code, but I've got a gist of all of the code examples in the talk already up on GitHub if you want to pull it up and go through it and run it later. I'll fly through these slides a bit, just pointing out some key features about how you implement the models. The key reason to do this is that whatever conceptual unity and harmony I may lead you to believe from my other slides, I want to convince you from the implementation slides that there are real challenges, computational challenges always, and getting this stuff to work. And I don't want you to walk away thinking like, oh, they solved everything. Solve some things. The insider view doesn't make your code work. It might help you understand and build code, but there are some real challenges to making this happen. So on the left is the statistical model. There's your stand code. I displayed the full stand code partly to show you that Stan commits the same sin, data parameters. We could relabel that observed variables, unobserved variables, that would make me happy. And then we have a model where we define the distributions for the unobserved variables. We compute this lambda thing from the other variables, and then we define the distribution for nodes in terms of it. The tool that comes with my book, Map to Stan, that's what the model would look like. That's how you specify it. And Map to Stan basically guesses what all the other data that Stan would need to build the Stan model. You with me? Yeah, okay. So first example, building on that. Let's think about generalized linear mixed model of birds, in this case. These are toy examples, but they're all chosen to teach one little bit about the unification of data and parameters and likelihoods and priors. So now we're going to imagine that every bird is a unique snowflake. There are a bunch of different birds in different rooms. And some birds are more fearful than others, and they react differently to cats than other birds do. And we've got some repeat structure in the data, so we're going to take advantage of this. This is a conventional hierarchical model of that, except I've made it as simple as possible by just using exponential distributions for all the random effects. So just very quickly, same model up top as before, except now we've got bird eye at time t and the lambda for bird eye at time t so I should with cat for bird eye at time t. And then there's a unique alpha and beta for each bird eye. Now we have to define distributions for the new unobserved variables, alpha i and beta i. And the means for these groups, these vectors of alphas and betas are alpha bar and beta bar. So new unobserved variables. Unobserved variables, alphas and betas for each bird now. Those are analogous to the previous ones. And now unobserved means of the population of birds. Typical hierarchical model. Good times. And same justifications on down. So very quickly, before I plumb the lesson about unification out of this one, I want to draw your attention to this great paper by Andy Gelman. This is a paper that I think isn't read as often as it might be because it has a really boring title. It's something like analysis of variance, why it's more important than ever. I don't know if you're like me when you see the words analysis and variance anywhere near one another. She can run in the other direction. And I had a really traumatic mascot's class in graduate school that was nothing but sums of squares. Endless sums of squares. I blacked out and I woke up a semester later or never to do analysis of variance again. But this is a really good paper. And in particular, in the second half of it, there's this great list of all the definitions of random effects that you might come across in the literature. And it's just maddening. So just very quickly. I'm not going to read these verbatim. So what's the distinction between fixed and random effects? Fixed effects are constant across individuals. Random effects vary. For example, blah, blah. Effects are fixed if they are interesting in themselves or random. If there is interest in the underlying population, site, site. When a sample exhausts the population, the corresponding variable is fixed. When the sample is small or negligible part of the population, the corresponding variable is random. So these are all incompatible, right? With one another. If it goes on, if an effect is assumed to be realized value in a random variable, it is called the random effect. I don't even understand that. What does that mean? Fixed effects are estimated using least squares. So now this is an algorithmic definition. And random effects are estimated with shrinkage. There are other possibilities, right? Anyway, so what's my point? I sympathize with the student who is frustrated in countering random effects and wondering what they are. Because from paper to paper, even within the same person, they could be defined in incompatible ways. So what I want to say is that, for me, what we usually talk about is random effects. It's just that they exhibit shrinkage. There's shrinkage. What does that mean? There's some mean of the group of parameters that share some family resemblance. They're the same kind of cluster of things. In this case, there are birds, and there's replication of the parameters across birds. There are family of them. And we model the mean of that, and that results in shrinkage towards the mean of the different birds. If there's a bird that has a really extreme observed singing rate, and there's not a lot of data, that estimate will be shrunk towards the population mean. And that'll give you a better estimate. This is a famous argument that I think is familiar to most of you. Non-Basian sessions use the same shrinkage estimators. Well, it's not the same estimator, but use the same shrinkage phenomenon all the time. This is not a Bayesian versus non-Basian thing. But shrinkage happens everywhere. You've got a distribution that's a function of parameters. Every time. There's nothing about random effects in a Bayesian model or in a non-Basian model that uniquely creates shrinkage. Ordinary likelihoods create shrinkage. It's just in that case you call it regression to the mean. Right? So there's this whole famous argument actually from an anthropologist named Francis Galton about regression to the mean, which produces the same phenomenon as shrinkage. So two quick examples. Just remind you, here's the empirical Bayes version of shrinkage estimators, the James Stein estimators. This is from Efren's, I think, great paper on these estimators from baseball players, American baseball players, where the best estimates of their batting averages are shrunk towards a common mean because of variations. So you can also think about this in a time series. You're trying to predict the player's performance in the next season, and you want to shrink extreme values towards the mean. The same phenomenon, of course, happens in Galton's famous trying to predict children's heights from their parents' heights. There it's called regression to the mean. There's no random effect or hierarchical structure to the model, but you get shrinkage anyway. It's just it wasn't called that at the time. It's the same statistical phenomenon, and it arises from exactly the same mechanism inside a Bayesian model, even inside a non-Bayesian model. It's because there are distributions, and those distributions are functions of parameters, and those parameters create gravity that attracts the family of things, whether they're residuals, in this case, or random effects in the hierarchical model case towards a mean. It's the same fundamental phenomenon. So I have found that this helps a lot in explaining to students what random effects are about. It's just regression to the mean, and they already understand that. At least the ones that I used to teach in California did. They were like, oh yeah, they understood regression to the mean. This is just regression to the mean, but now among parameters rather than among data points. So there's some conceptual delivery from the unity, I hope. Here's how you implement this model. I think this will be familiar to a lot of you to see how it goes. Again, we've got the knotting words, data, and parameters, and we add in the varying effects, vectors, alpha and beta, and the bar terms. The model doesn't change very much. Right. Okay. Plowing forward. Now, let's get into a couple more examples where they have the flavor of the kinds of data problems that I work with in my own research. And these are cases where we don't have full measurement control over the things we normally call data. Sometimes that's just because of the nature of the phenomenon. There's irreducible uncertainty, and sometimes it's because, well, studies could have been better, but weren't. And we just want to get what is there. So before I get into that, let's revisit the previous model and let's just add a couple of lines to it to say that we're going to jointly model, at the same time we model the bird's behavior. Remember, the birds are singing. What are the cats doing? Well, the cats are entering and leaving the room. This is a great life for the cat. And I told you it was a toy example. And the cat is entering and leaving the room. And so we want to estimate the cat behavior. How often is the cat around? And we can write down a distribution for that, too. So now we've got the cat at time t is distributed as a Bernoulli variable with some probability, and we give a prior to Kappa beta distribution with some regularization. The 4, 4 makes it so that the ends have probability 0. Kind of shape like that. Oh, I've got it on the slide. There it is. So far, this is just a bigger joint model. Now we're jointly modeling both animals. But if we observe all the variables, now it's just simultaneously running two regressions. Nothing too special about that. You can do it. The real value of doing something like this comes when you don't always observe the cat. So let's start with the simplest example. Say, sometimes there are missing values for the cat. And I have this, blame it on the cat in this case. Say the cat steps on the keyboard occasionally and gets an NAs, right, in your data set. Or it's your research assistant. Blame who you are. In the sort of data I work on, this happens for a whole variety of reasons. Sometimes it's because one of the people collecting the data forgot to record a variable. And so you get a whole day where a variable is missing. It happens. And then you can't send them back to the field because the field is Singapore. And it's fairly expensive to just send them back. And that's how it goes. So now the nice thing is this model we've defined, it's a joint distribution of all the variables, automatically lets us handle the missingness. But here's the thing, cat now is data or parameter depending upon whether the value is missing at that spot. It is both things. And the distribution, the Bernoulli distribution on cat sub t is both a likelihood and a prior in the same model. And it solves the problem for us. Now it doesn't mean it actually tells us exactly whether the cat was there or not. That depends upon the data. But it gives us a statistical solution to the missing data problem. So here's how you define this in stand to deal with the missingness. You've got to, I'm not going to walk through this code in detail just to say it's on the gist and you can go through it. In stand, I marginalize over the discrete missing variables. These are like the indicator, the interaction indicator variables in the morning keynote. You've got to ask if the cat value is minus one. That's just the internal code for missing. Then we do a mixture over the two possibilities. Otherwise, we observe it and then we just do the two regression distributions. And there's also, let's say in map to stand, if you use the exponential branch that's up on GitHub, it will take this model definition and build that. It recognizes the binary missing variable and builds the mixture model from it. But you've got to use the experimental branch and I make no promises that there are not bugs in the experiment. So it's called experimental, but I use it every day. So that's all I can tell you. You can get the cat, the posterior probabilities the cat is present or not in the cases where the cat data is missing by using this generated quantities trick in stand as well. But stepping past the computational challenge, you can get, depending upon the data, you can get information about, sometimes reliable information about whether the cat is present or not. So now I've got cat in Pute 1 and 4 in the cases where, in my toy example, the cat was missing or the data on the cat was missing. We don't know if the cat is actually missing. And in one of those cases, the cat is probably present, but we're not sure. The amount of singing by the bird leans in the direction of the cat being present, but it's not a slam dunk. And in the other case, the cat is almost certainly missing. Still with me? Yeah? There will be a summary at the end. So we're getting there. So final example. Now let's think about an example that has elements of all the things we've done so far. So same joint model, but now let's consider the issue that the cat is not stepped on the keyboard. So there are no actual NAs in the data set, missing values. But what is true of every cat observation is that you can't necessarily trust it because cats are good at hiding. Sometimes the cat was in the room, but the person who had the data sheet couldn't find the cat. The cat was waiting to jump out at the bird or something like that. So let's imagine, again, toy example, let's imagine the bird always knows the cat is there. Because birds are smarter than people. But the person doing the data logging doesn't always know if the cat is really there or not. So you can trust a one. When the cat variable says one, the cat was observed. There's no phantom cat that was observed. But when the cat is zero, you can't believe it. Now the zeros aren't data. They're data of a kind, but it's not the variable you're interested in. There's a latent variable that you actually want to observe, but can't, and that's the true state of the cat. So this is make Schrodinger's cat jokes now. It's the cat in the room or not. And so we're going to do this statistical version of Schrodinger's cat. And so this is the statistical version of that argument. Now we have let cat sub TV the true state of the cat. It's in the box. We can't see the true state of the cat. What we get to see is cat observed at time t, and it has a Bernoulli distribution where it's the probability that the cat is observed is a product of the true state of the cat whether the cat's there or not. This is a zero one indicator times the detection probability. So when the cat's absent, it's always zero, and you never see the cat. When the cat's present, you only see the cat delta at the time. Yeah, you with me? Those of you who have cats, does this resonate with you? You don't always know. And then the rest of the models are the same as before, except we have a prior, or I should say, distribution on an observed variable for delta at the bottom. In ecology, we call these occupancy models. They do a lot of heavy lifting in field ecology, and they become really important in endangered species studies as well. So the implementation of this before I get to the key thing about it is even more complicated just showing you the model block here. There's lots of commentary if you want to read this later to understand how it works, but like the previous one, this is a mixture. There's multiple likelihoods for each of the possible missing-ness states in it, and you have to average over the inside stamp. But it works great, and you can get estimates for both the frequency with which cats are present and the detection probability of cats out of things like this. This is useful data. So at my institute, we use... I mean, these are toy examples that I've given you today, but at my institute, we use models exactly like these, almost exactly like these, in real research, not on cats and birds, but on chimpanzees. And there's this big project called the Pan-Africa Project based at my institute, which has about almost 1,000 camera traps across territorial Africa, taking photographs of anything that walks in front of them, actually videos of anything that walks in front of them. And so there are hundreds of thousands of videos. Most of them are not apes, but then there are thousands of videos of apes doing things, and we're interested in the distributions of behaviors among the apes, but we simultaneously need to estimate the population densities of the apes. And both the behaviors and the population counts are subject to the same uncertainty that you observe in shooting your cat that goes on. So we use these models in modeling this camera trap data as well. And you need to do it because ignoring the detection probability is a disaster. You get the wrong answer. You undercount things. That's the problem with it, right? Okay, so let me try to summarize here. So the general argument is there is virtue in taking the insider view on apes in unifying concepts that are split in the outsider view of apes, and these are the distinction between data parameters and the distinction between likelihoods and priors. Of course, there are times when it is useful to distinguish these things, absolutely, but there's also a lot of conceptual value in seeing them as fundamentally the same thing inside of a Bayesian model. So the first example I gave you today, the point I wanted to get across was both likelihoods and priors are distributional assumptions on variables, some observed or unobserved, respectively. And these distributions can be derived from the same informational perspective. There's an information state. What's the metadata on the variable before we've seen its value? And of course inside the computer, when you run calculations, you treat them the same way. You can't, in the outsider view, a likelihood is not a probability distribution, but of course it's calculated exactly as if it was one. And we write it in the mathematical model as if it was one. And that's because in Bayes it is a distribution, but over data, not over the parameters. The second, both likelihoods and priors induce the same inferential force, that is they cause shrinkage. And when it's a likelihood, in the outsider view, you call it regression to the mean, and when it's random effects, you call it shrinkage, but it's the same basic phenomenon that the distributional assumption induces skepticism and inference for extreme values. And it takes more evidence to overcome that skepticism, and that's what causes the shrinkage. And it's good, it gives you better estimates. Regression to the mean is a good thing statistically. It improves your predictions. And just as shrinkage on random effects improves your predictions. The third example, what I wanted to get across is that distributions do double duty in models. They can be simultaneously inside the same model, both a likelihood and a prior. And the same variables can be both a parameter and an observed variable inside the same model, depending upon the details. You start with a joint model, a generative model of the system, and then things happen. And the Bayesian framework takes care of the conceptual difficulties of trying to sort out data from parameter and such. That said, it doesn't take care of the computational challenges, which are substantial at times. Absolutely substantial. So again, and then the fourth I think I already said, that even inside the same analysis, the same symbol can be both data or a parameter. The same distribution can be both a likelihood or a prior. I want to say before I move past this slide that there are of course cases where it's very important to distinguish data from parameters or rather observed from other variables. Absolutely. And if you write your own Markov chain, you know of course you have to make proposals for one of these things and not for the others. So it's a very important difference in all the bookkeeping that goes with that. But all I'm arguing is that in teaching this and understanding model construction and interpretation, the unifying perspective is very important. So this is the kind of slide that I put up on the ends of talks to serve as a summary. So it's got way more text than I would normally put on a slide, so your apologies. But I've learned over time that people like summary slides that have a lot of stuff on it. So let me try to summarize very quickly the benefits of the insider view and I'll read this quickly, but you'll have access to these slides later if you want to study them with a glass of wine sometime. We're going to take the insider view. So the insider view is not necessary. The philosophy in general is not necessary, but it is useful. What I find about it that's useful is it helps me to think scientifically, not statistically. It makes me think about the joint model of the system and how the data is produced and I can engage with that and I get a model that will work for all kinds of combinations of missingness and uncertainty. I can build off of that and make a model that isn't statistically ad hoc. You can get data sets having already had a model and you can see what you can infer given the data you have at hand. Many solutions to common science problems arise directly from this approach. I call measurement methods which are true of all the projects I work on. They're measurement error problems because it's often field data collection. And it's very important for me and all of us, of course, to propagate uncertainty in the analysis, to not shed the noise around an estimate as we move through a project and the Bayesian approach makes that a lot easier to do. But, yeah, the computational challenges are very real. Sometimes it's difficult or impossible to fit the model we'd like to fit and we have to make compromises. But it's good to get your philosophy organized first and make wise choices about those things. Unified approach to construction of both likelihoods and priors is said before. What I like about all of this is that I personally find it demystifying and deflationary. Statistics is over-hyped, right? And leased by statisticians, but most outside of statistics. And the deflationary view says, look, this is a garbage-in-garbage-out project. You define the joint model of all the variables. All Bayesian inference can do you is tell you what the data says about that joint model. And that's all. And then there are no guarantees. We're guaranteed we'll not be offered. And I like that. I really like that it's a humble perspective that is nevertheless extremely powerful at the same time. Okay, so this is the final slide, which I mean to be a conversation starter. Say I want to make a modest proposal with all the implications, literary implications of that title. There are a bunch of conventional terms that we use in teaching Bayesian statistics and appear even in my own book. And I suspect that it's a mistake to continue using them, at least without qualification. And so it would be nice to, as a community, those of us who are interested in Bayesian statistics, applied or theorized to think about alternatives or families of alternatives to better teach this material because the population of people who want to use Bayesian methods is growing very fast. This is the time to get in front of this problem and think about developing new teaching materials that can make this better. So, very quickly, and then I'll end my talk, data to the observed variable. A parameter is an observed variable. A likelihood is just a distribution. I'm least sure about a prior is just a distribution. I'm not happy with that necessarily because sometimes you do want to make a distinction, but I'm not happy with the term distribution even because people have mythical ideas about what that means. I think people think distributions are sampled from. That's what makes me nervous. State of information would be an alternative, but no one knows what information is either. So that's including me. So posterior, can we call this a conditional distribution? If we're going to get rid of prior, then there's nothing to be posterior to. So this doesn't roll off the tongue, so we need some solution here, and conditional state of information would be even worse. Then we have terms like estimate and random, which I like to vote for banishing them, voting them off the island. These are terms that seem to do nothing useful for us, except cause problems. We don't have estimates in Bayesian inference. We have posterior distributions. Then there are things we can do with those posterior distributions which lead to behavior changes given some decision model, but we don't have estimators in the traditional sense. The word random just causes a lot of problems. Anyway, thank you for your indulgence, and I hope that was useful.


I'm Ivana, I'm currently studying a Bachelor of Laws in Criminology and I'm a Mara Mollie Scholar. Today what we're doing is a Chinese exchange, so we're looking at different cultures, it's a cultural exchange. We're looking at Australian culture, seeing the iconic things, we're looking at iconic foods, cultures, the slang, and it's a great opportunity to meet other Mara Mollie scholars from Hangzhou Normal University and it's an incredible opportunity that I'm so grateful to have.


Hello everybody. Andrea here with the Whitening Pro Academy. I'm going to discuss the three steps that you need to really think about and get going once you're ready to start your own teeth waning business. So I'm talking specifically of your own teeth waning business in your own home and or mobile to see your own clients. You could also rent a separate space somewhere else in a building somewhere or just simply add it on to your current business. If you're a hairstylist in the beauty industry, there are so many different options. But step number one, depending on where you live, you will need to maintain a master business license. This is called something different in every state, every area, but basically you need a business license. This proves and is the official way of saying that you have your own business. So I suggest talking to an accountant and they will be able to help you out with that. You will need to find an accountant anyway. So now is a good time to get started.  If you're making income, it could be up to $200 per hour per client. You're going to need an accountant to help you organize everything. Step two is think about taking out a loan if needed. So this is up to you. You can, you may or may not have to.  They truly, truly don't sign up for my whitening pro academy course. I send you everything that you need for your first 10 clients and that's all included. It is about $1,600, you guys. That's it. So if you don't need to take out a loan for that, fantastic. You can literally get started right away. Once you need refills on anything, then you can purchase them after you start seeing clients. So you will be able to easily afford them because you will be making $200 per say per client per hour. So easy. Plus through the whitening pro academy course, you get full access to a wholesale account. So your products are much cheaper anyway. So it is the way to be. And step three is to really sign up for a teeth whitening training course in a lot of areas. You cannot be a teeth whitening technician without the proper training. That should actually be step one, I suppose. But think about it this way too. You want full support for your new business. So the whitening pro academy isn't just teaching you guys how to apply peroxides to your client's teeth. There's a full business component. So I teach you guys first all of the theory, all of the practical components of how to safely and effectively whiten your client's teeth, but then also how to have your own business, how to get organized, how to do your own bookkeeping, like how to keep track of income, expenses, how to save money so you don't have to hire people to do that. I even teach you guys how to make your own simple website if that's what you want to do. I teach you guys about Facebook pages, Facebook groups, Instagram pages, really how to market your own business. I teach you guys how to make your own logos, thumbnails for YouTube like I'm doing, if that's something you want to do. I teach you guys how to make your own business cards, your own consent forms, medical history forms, all of that. So I teach you guys literally everything you need to know. So you don't just know how to whiten teeth and then go, now what? How do I get clients? How do I make my own forms? How do I do this? How do I do that?  Literally every month we need online to talk about your business, questions, answers, anything you need. I am here for you. So this course is truly for life. The theory portion is also learn at your own pace. So you learn everything online. It might take you two weeks to learn everything. It might take you two months. It might take you two years. Take your time, but it's learn at your own pace. And once you do sign up and pay in full, you get everything sent to you right away. Shipping takes two weeks, maybe three weeks depending on the location and these days depending on the weather. But you get everything you need to get started. And I also help you if you want to have your own teeth-winding business in your own home or and if you want to go mobile to clients. So I teach you guys about certain insurances that you might need. I teach you guys some of the basic extra equipment that you might need if you're seeing patients in your own home or if you're traveling mobile. Say you might need a cart. You might need an organizational system. I teach you guys all of that. And I also show you exactly what I have because I have my teeth-winding business in my own home here, but also mobile as well. So copy me. You can buy everything I do, you guys. I teach you guys everything. But again, in the full course, I send you everything that you need for your first 10 clients, masks, bibs, everything you need. So I make it as easy as possible for you. So if you've been thinking about starting your own business, if you've been thinking you don't want to work so hard 9 to 5 for somebody else, you want to have your own business, make your own schedule, make your own money, make good money, I can teach you guys how to do that. So please let me know if there's any questions.  Sign up for the course because Enrollment is now open and I will talk to you guys very, very soon.


The following is a production of New Mexico State University. Today's gleaming chemistry and biology labs at New Mexico State University are far different from the first facilities at what was then called New Mexico College of Agriculture and Mechanic Arts. The agriculture curriculum once contained all classes in chemistry, meteorology, botany and human physiology. Seniors wrote thesis papers to help document the plants and insects in the wild territory. Classes were taught by everyone, including the college president. The registrar even wrote an early horticulture bulletin. Professors built furniture to equip their crowded and sometimes dangerous labs. College documents report one fire with an explosion that blew out the window glass and scorched the chemist somewhat. For the early years, I'm Carla Aragon. The preceding was a production of New Mexico State University. The views and opinions in this program are those of the author, and do not necessarily represent the views and opinions of the NMSU Board of Regents.


I have a deep question, not so philosophical. Deep but not philosophical. I was taking notes, occupied takes actually, in a run of art pen. Okay. I'm a, by the way, member of Ethics Committee of the Berthelen Party of Russia of the Federal Committee. Okay. So, I'm not going to argue about the pace, and I just have one question. Have you actually read, I am writing in the book of her? I will, I will. Yeah. Yeah. It doesn't feel like it did, because one of the major takes of Iran is the plus struggle between oppressor and nomenclature, each of us. She's ex-soviet person, right? So, she perfectly knew what she's talking about, right? So, James Taggart, he was just, David Taggart, Taggart, right? It's not one country he needs, another country. Surprisingly, for a person who's president, fine, Andrea Vincitute, you take a lot of takes about how one country is better than another country. Like, I'll let you quote too. Basically, free countries. Yeah, I believe some countries are better than other countries. I mean, you don't have to quote me. I'll say that again. So, the Iran Bay is that almost any country as a statist organization is bad against its own people. Like, let's say you talk about free speech and political prisoners is what qualify, it basically disqualify, it basically frequent country in a authoritarian country. So, what's your take on Julian Assange, for example? Well, Julian Assange is a criminal for a variety of reasons. I'll tell you exactly why Julian Assange is a criminal. Snowden is a hero, but Assange is a criminal. So, first of all, it's pretty ridiculous to accuse me of not having read Iran when you clearly are completely ignorant of Iran's writings. She talks about differences between countries all the time. In all her writings, in all her essays, she talks about, she even makes comments about Israel and the difference between Israel and other countries. In Israel at the time when she made these comments was a socialist country, and yet she viewed it as a superior country to other countries.   He is willing to publish anything, including stuff that would harm human life, that would destroy the capacity of free countries to protect themselves and defend themselves. He was willing to publish trade secrets of corporations, anything that's secret. He is willing to publish, including violation of property rights, which is trade secrets and corporate information, which is none of his business and is not in the public domain and the public has no court right to know it. He is not a defender of freedom and freedom information or anything like that. He does not have a concept of freedom. He doesn't have the concept of individual rights or concept of property rights. You're talking about why freedom is a concept free of coercion. Did Julian Assange curse somebody to obtain this information? Yes, he stole stealing his coercion. He stole, he, okay, other people stole it and he published it.   So, once you are facilitating crime, so Julian Assange was facilitating crime by publishing stolen material.  I don't think there's any question. Snowden, on the other hand, clearly identified areas in which the United States were violating the individual rights of its own citizens, made sure to take out of what he published that which could harm agents and people in foreign countries that might have been harmed by the release of the information. Tried to go through the channels to get things, couldn't do that. So, he released information. He's a hero. And I would... Yes, but he stole from those who do not have a right to keep it. Which is, in your opinion, if there is a moral right to... So, if you say, if you steal, but for good, like Robin Hood would do it, right? No, Robin Hood's a criminal. Right? Robin Hood's a criminal because... He's a morally justified crime. He's morally justified to steal from the government in order to reveal the government's criminality. It's not... Assange didn't do that. Assange would publish anything. And Assange would publish anything. And it's not morally okay to steal from private businesses. But I don't want to... So, that's my opinion on Assange. You asked for it? You got it. I don't want to get into an argument about it. In terms of differences... This is a problem with libertarians. The problem with libertarians, and you can see this in the new Mises Caucus in the American Libertarian Party right now, the problem with libertarians is you cannot make distinguishing differences between countries.  I mean, he used to celebrate every time an American pilot got shot down during the Vietnam War. You can be anti-war without relishing the idea of Americans dying there. You can be anti-war without wanting the North Vietnamese to win when North Vietnam took South Vietnam, when they united Vietnam under communism. Libertarians in America celebrated. This is why I don't call myself a libertarian. This is why I don't want to be associated that much with libertarians, because I think that's disgusting. If you can't see the difference between communism, between authoritarianism, where you can't speak, between Putin's Russia and Japan and the United States, then you're blind. And you're making yourself blind because you're not blind. You're making yourself blind. Am I making yourself blind? You're destroying yourself and by doing this in the name of liberty and freedom, you're destroying the liberty and freedom movement. And that's why nobody will take you seriously. So, of course, there's a fundamental difference between if I say something and a policeman comes in and drags me off to prison. There's a big difference between that, that plus all the other coercion, and where the coercion is limited to one sphere, let's say taxation or economics. It's still bad. It's still evil. But it's a different degree of evil. It's far less than a police state is. So, yes, I value countries. I would rank them. There's an economic freedom index for a reason. So, you can rank them in terms of how free they are, and you can still condemn them all. And countries are legitimate. Ayn Rand was not an anarchist. Ayn Rand did not believe in anarchy. She argued against anarchy. She called libertarians in the 1970s hippies of the right, which was not a compliment. She advocated, she loved America. She loved America as a country. She loved America in spite of hating its politicians. And she thought it was an amazing country. And when she compared it to the Soviet Union, she thought the Soviet Union was fundamentally evil. And she thought America was fundamentally good, in spite of the fact that there was still coercion going on. That's Ayn Rand. You call Japanese, for example, a Japan basically free country, right? So, right after Snowden, your favorite guy, they passed the law, which basically prevents things like Snowden ever happening again in Japan. It doesn't prevent Snowden violated the law. So, passing a law against Snowden doesn't help. The whole point of Snowden is he violated the law. No, no. I mean, that's the thing. I mean, it's actually a sign. You can't have a law that prevents Snowden from happening. You publish, if let's say you're Snowden and you leak information from Japan, and you give it to me, and I publish it, we both go to prison for three reasons, forever. Right? So, there is no freedom of speech in that sense at all.  Like, I don't know what to say.  Or like, they have to, for example, stay divorced after a divorce for like, almost a year, because, you know, who knows. So, Japan could be freer. It's so much freer than Russia. That's the point. Yes, of course. There are more aggressive regimes than others. That doesn't make you more taken moral stance saying like, oh, US is all correct, and Russia is all wrong. Nobody said, you will never hear me say. You will never hear me say the US is all correct. You didn't mention a single example of US. Your whole lecture was about how terrible China and Russia is, which is pretty much China and Russia are terrible. Yeah, but like, US is comparably terrible. US is not comparably terrible. No, we're near as far as Iran war and Iraq war was totally justified, same as Ukraine war, right? There's a massive difference between the one you are, massive difference between the one you are talking about. Let's talk about Israel. In West Bank, if you enter a relationship with a Palestinian lady, you have to notify the Israeli government and take a 27-month-old. You really shouldn't talk about things you don't know anything about. Oh, yeah. People really do, yeah. Yes. Thank you for listening or watching the Iran book show. If you'd like to support the show, we make it as easy as possible for you to trade with me. You get value from listening. You get value from watching. Show your appreciation. You can do that by going to iranbookshow.com slash support by going to Patreon, subscribe star locals, and just making a appropriate contribution on any one of those, any one of those channels. Also, if you'd like to see the Iran book show grow, please consider sharing our content and, of course, subscribe. Press that little bell button right down there on YouTube so that you get an announcement when we go live. And for those of you who are already subscribers and those of you who are already supporters of the show, thank you. I very much appreciate it.


Hey, this is Brett and this 2017 Chevy Silverado 2500 Crew Cab Short Box LTZ is stock number 13027Z. I'm here at Summit Automotive in Fond du Lac, Wisconsin, you're new and used heavy-duty truck headquarters. This 2017 Chevy Silverado 2500 has the 6.6 liter Duramax diesel engine. It's the L5P engine which puts out 445 horsepower. It's combined with the Allison heavy-duty six-speed automatic transmission. This truck has been fully safety and inspected by our service shop as a fresh oil and filter change, all the fluid tab been checked and topped off per the state of Wisconsin inspection process and this truck is 100% ready to go. I'm going to go all the way around in this video inside underneath, start it up and take a look under the hood. Red hot is the color and I shoot all my videos in 4k so if you have HD capabilities on your computer, tablet, smartphone, or television I highly recommend turning them on right now because it is your best way to check out the quality, condition, options, and cleanliness of the vehicle before seeing it in person. And if you like the video and how I do things here at Summit Automotive consider clicking the subscribe button on my YouTube channel in the lower right hand part of the screen and then click the bell notifications and you'll get updates on the videos I do each and every day here at Summit Auto as well as a large catalog of videos on vehicles, one of the largest on YouTube. Comes with the 20 inch painted and polished aluminum rims. These are the factory rims. Some of my favorite rims on the Chevy's has Goodyear Wrangler SRA tires. These are LT 265 60R 20s and they have right around half the tread left maybe just a hair under. Frame and underbody is exceptionally clean on this truck for being a 2017. Front fender is in fantastic condition. I didn't see any major dents or dings on there. Comes with the projector lamp headlamps, factory fog lights, and the front bumper parking sensors. You get on here and the front bumper is in fantastic condition. I didn't see any major dents or dings on there. Lower valence looks really nice and it does come with a chrome trimmed grille. The hood is in fantastic condition as well. I didn't see any major dents or dings on there and this is the first year that you could get the coal induction hood since it was the first year of the L5P engine and this one is actually functional on the Duramax. So I'll show you how that works in just a little bit at the end of the video. Coming around to the passenger side no major dents or dings on that fender and the passenger side rim no major scuffs or scrapes on there and that rim is in very nice condition. I didn't see any corrosion on there. As you go down this side of the truck take note of how clean the body is, how reflective and mirror like that paint is. I take these HD videos so if you are far away or even if you're close by and you just cannot make the trip down but you're still interested in purchasing the vehicle you can see the truck, hear the truck, and have confidence in the vehicle that you're looking at before you even get here so when you do get here there's absolutely no surprises and you can make a smart and informed buying decision from wherever you're at and if this video helps you make that buying decision let your salesmen know that you saw the video that it was helpful and that Brett sent you and if you like the video and you can subscribe to my youtube channel the upper right hand part of the screen comes with the back rims 20 inch rims in the back as well they're in fantastic condition too and the back tires have just as much tread as the front tires maybe just a little bit more tread than the front tires. Framing underbody once again exceptional condition I didn't see any corrosion on there which is pretty rare must be a southern truck we'll check on that in just a second lower underbody has all the remaining factory exhaust lower rockers all look really good as well and it does come with the very nice factory chrome step bars down the passenger side box didn't see any denser dings and coming around to the back rear bumpers in fantastic condition does have the full towing package which includes a receiver hitch four pin and seven pin wiring backup parking sensors and rear bumper steps tailgate is in very nice shape does have a locking tailgate shock down assist tailgate spraying bed liner you also have led bed lighting up there those turn on with the cargo lamps and the beds in fantastic condition didn't see any major denser dings back there tailgate shuts nice and solidly and as you go down the driver's side just as clean as that passenger side does have the mud flaps which keeps your lower rockers looking good and the driver's side box just as clean as that passenger side no denser dings on there and for full disclosure this back rim just as nice as the rest and down the rest of this side of the truck doors and cab all look really good does have the telescopic tow mirrors built in directional signals led side lights they do telescope out like so and fold in and my guess would be that they power fold in which they do inside the LTZ package gives you the gray leather interior there are no rips there are no tears on the seats they're in very nice condition does have um they are air conditioned and heated both are power max liner all-weather floor mats auto headlamps turned out four-wheel drive factory brake controller tilt telescopic steering wheel smells very clean inside this truck I think it's ever been smoked in those to get power windows power locks power mirrors and these mirrors do power fold in like I said I always like showing both sides so that you know that both sides are working properly and last but not least you got memory driver's seat and Bose sound system take a look at the back seats just as clean as front no rips or tears back here it does have the latch child safety system for any child car seats you may have power sliding rear window with the built-in rear defrost those seats are in great condition they fold up all weather floor mat back here as well which keeps your carpeting looking like new side curtain airbags and bottoms of the doors all look really good we'll hop inside and check out the miles the radio and everything that this truck has to offer and then we'll start it up and take a look under the hood so this one has 55,160 miles you do get a digital spinometer compass display and that instrument cluster is very nice and clean comes with the heated leather wrap steering wheel bluetooth and information center controls on the right bluetooth i'm sorry bluetooth and information center controls on right cruise controls heated steering wheel and forward collision controls on the left comes with the allison heavy duty six speed automatic transmission with the optional tap shift this one does have the chevy my link system you get the factory navigation system on there am fm and serious xm radio capabilities it also has a projection manager where you can project your cell phone to the screen via android auto or apple carplay and you can also this is also where your backup camera shows up i'll show you that in just a second down here you get a cd player radio controls heated and cooled seed buttons dual climate controls power pedals stability control that's for your cargo lamps it's also how you turn on those led side lights and led bed lights you can turn those parking sensors off and on lane departure warning and your factory exhaust break is right there two usb's two 12 volt power points and a 110 volt 150 watt plug-in passenger side format and seat are in fantastic condition i didn't see any rips or tears on there the headliner is in nice shape i didn't see any rips or tears on that you do get map lights up there power sliding rear window button and your homelink buttons for your garage door security systems and lighting systems on star and so s buttons in the and this one does have the wireless cell phone charge pad which is a really nice feature all right we'll start it up and take a look under the hood starts right up no check engine lights or anything like that there's your backup camera that's working nicely and we'll take a quick look under the hood there are those led side lights they are super bright and i would personally like to thank you for checking out the video today and hopefully from this hd video you have been able to verify the quality condition options and cleanliness of this truck all the way around inside and out under the hood we have the 6.6 liter duramax diesel engine engine bay is very clean runs very smooth once again this truck has been fully safe and inspected by our service shop as a fresh oil and filter change all the fluids have been checked and topped off and this truck is 100 ready to go 445 horsepower there is your emissions sticker and the air comes in from the cold air intake goes right to here goes into the air box right there i did want to show you the tire and loading information sticker real quick as well as the vinn sticker i apologize for forgetting this anyways there we go and i would highly highly recommend this truck from a quality and condition standpoint i didn't see a single dent of ding on it i think it's in fantastic condition whoever gets it will be happy with it wouldn't hesitate to ship it to california or florida right now and to see more pictures of this truck or one of other phone or 50 new and used cars trucks scvs minivans wranglers half tons three quarter tons one tons you name it we got to go to that website right there is summit auto dot com full pictures and descriptions of every single vehicle from two locations all at summit auto dot com if you like to check out more hd videos you can go to youtube dot com slash summit auto number two like subscribe and share on this video and all the videos that you see there click the bell notifications you'll get updates on the videos i do each and every day here at summit auto in fact in a second you will see link to subscribe my youtube channel the upper left link to more Chevy 2500 truck videos like this one the upper right link to this vehicle on our website in the lower left and a link to one of our latest youtube videos in the lower right click those check us out and i'm super excited to help you with this we're super excited to help you with this ultra clean 2017 Chevy silver out of 2500 crew cab short box LTZ in red hot clear coat thanks again for checking out the video remember to like subscribe and share on my youtube channel i really appreciate it thanks again