Welcome to Lecture 17. I want to start by talking about rituals. March 1st, this year, 2022, is Shrove Tuesday. And on Shrove Tuesday, many Christians burn things. For example, palm leaves, or in places where palm leaves aren't available, other kinds of leaves. What does this ritual mean? Well, of course, it has a symbolic meaning that's tied to Christian history. But what it really means is its function to the community that practices it. That's the importance of the ritual. And it can have that function even if the people participating know nothing about the biblical story in which it originates. The other thing that is traditionally burned on Shrove Tuesday are pancakes. They're not intentionally burned, not usually, but nevertheless, lots of them end up burned. And this leads us to another aspect of meaning and understanding and function. That is, the function of probability theory does not typically require that we understand the results it produces. Let me try to explain that with some pancakes. So imagine that I cook three pancakes, and I burn two of them. One of them has been burned on both sides, there at the bottom of the screen. Another, I've only burned it on one side. I was starting to get better. That one's at the top of the screen. And then, by the third one, I had actually figured it out, and I have a perfect pancake that's not burned on either side. So now, you come to my house and I serve you one of these pancakes at random, and the side facing up is burned. And now the question is, what's the probability the other side of this pancake is also burned? This is a version of a classic probability paradox known as Bertrand's Box Paradox, but we can call it Bertrand's Pancake Paradox. It's a paradox because intuition does not work here. It's extremely difficult for people to intuit the right answer. And even when the right answer is explained, it's often very hard for people to hold on to it. But probability theory gives us the right answer. So let me walk through this just to start. So to remind you, here's the setup. There are three pancakes. The first one on the left here is burned on both sides. The second one's burned on only one side. And the third is not burned on either side. You are served a pancake and you can only see the side of it that is facing up on your plate. And that side is burned. What's the probability the other side is also burnt? Most people, the vast majority, even those educated in probability theory, say that the probability is one half. And that's wrong. The intuition being that there are two pancakes that have burnt sides, so it has to be one of the two. It's just random like a coin flip. But this is not the right answer. Let's derive the right answer and we're going to do it by resisting the temptation to be clever. And we're just going to use the axioms of probability. So let's just start with the definition of conditional probability. The whole deal with probabilistic inferences, we condition on what we've learned to figure out what we don't know. I'll say that again. The whole principle with probabilistic inference is to condition on what we have learned to see what the implications are for what we haven't learned. And so that means we use conditional probability. And the definition of conditional probability gives us the formula we need in this case. And that is that the probability that the other side of the pancake, the downside, is also burnt conditional on the upside being burnt. This is the question is equal to the probability that both sides are burnt. That's the probability of burnt up comma burnt down the joint probability that both sides are burnt divided by the probability that you get a burn side facing up. And we can calculate these two terms. The top one here, the probability of burnt up and burnt down is just one-third because it's one of the three pancakes, right? Only one of the three pancakes has both sides burnt. So the top here is one-third. What's the bottom? We can calculate the bottom again using the axioms of probability by averaging over the possibilities. So there's a one-third chance of each pancake. And if it's the first one, there's 100% chance that the burnt side is up, right? If you're served at random, the pancake where both sides are burnt, then whichever side ends up being flipped up, it will be burnt. Next, in the middle, if you get served the pancake where only one side is burnt, then only half the time will the upside be burnt. And then finally, on the right, if you get served luckily the good pancake, then no matter which way it's flipped, the upside will never be burnt. You do the arithmetic here, and the probability if you're randomly served a pancake that the upside is burnt is one-half. We can put these two bits of the answer together. One-third divided by one-half is two-thirds, and that is the correct answer to Bertrand's pancake paradox. It's paradoxical, again, just because intuition does not grasp it. Intuition leads us very strongly to another answer, and even once we've got this answer, it somehow doesn't seem right. If you look in the book, I give you a short simulation to prove another way that two-thirds is the right answer, and yet still many people, myself included, after having seen this answer and derived it myself multiple ways, it still does not seem intuitive. If you want a little bit of intuition, though, a trick that only works in this case is to realize that it isn't the number of pancakes that are burnt that matters. It's the number of sides that matters. We're interested in the sides, and there are three burnt sides in the six sides of pancakes here. The reason I introduced this pancake story is to prime you to think about how probability theory works and how its function does not really rely upon us grasping its meaning in a particular way. In fact, it's not clear that that's even a meaningful question to say what the meaning is of a set of logical axioms. Being clever in scientific reasoning is incredibly unreliable. It's also opaque, and that opacity means that no one else should trust your clever solution. It might work in some particular case, but not in another. It's much better in nearly all cases to resist the urge to be clever, to show off, to signal, and instead just be ruthless, ruthlessly follow the axioms of probability. Probability theory provides solutions to problems like the pancake problem, but also real problems if we'll only follow the rules. And in this lecture, I'm going to show you some very important and extremely common data analysis problems where probability theory gives us essentially automatic solutions to them if we'll only follow the rules of probability theory. And often, when we do these, when we follow these solutions that we get just by following the rules, the results are sometimes paradoxical. It's not entirely clear why it happens the way it did because our intuitions would have guessed something else would happen. And again, that doesn't mean anything is wrong. Often there's nothing else to understand in this business except that the meaning of the results is the axioms themselves. They're the things that engender the results, just the logic that comes from it. In the lectures last week, I already showed you an example that involves the rich elements of real data analysis, these Gaussian process regressions where we have measurement error and underneath it there's some complex process going on we're trying to learn about and there are many, many possibilities under there where it's coming from. And in the lecture today, we're going to pick up from here and think about measurement error as a big area on its own. It's present to nearly all scientific projects and all research projects and we should take it seriously and think about some principled ways to deal with it. This will also take us all the way back to earlier weeks in the course. I think it was the third week where I introduced the four elemental confounds and the fourth one here, the descendant, has not been mentioned as often as the others but at the time I did say that it has something to do with proxy variables and measurement error and it's going to play a leading role today. Truth is that many of the variables we analyze in statistical projects are actually just proxies of the causes of interest. They're imperfect measurements, ghosts of the things that we'd really like to see and it's extremely common, as in many of the examples up to this point to simply ignore measurement error but we know that that is not always safe and so there are also many ad hoc procedures for dealing with measurement error but these can be unreliable because they rely upon cleverness and intuition and while they may work in isolated contexts, they will not generalize very well. It's better to think causally because of course measurement is a causal process and the mechanisms that produce measurements are things we can model generatively just like everything else in the systems we study and if we're willing to do that, make generative causal models of measurement then we can lean on probability theory to tell us how we should analyze those measurements. I'd like to prime our thinking about measurement error with a very simple example and then we'll build up into more complicated measurement error projects that are more realistic. In this example I want to attack a particular myth that is common in the sciences which is that measurement error can only reduce the size of an estimated effect. It'll never increase it and so you'll read, for example, that if there had been measurement error it has simply reduced the size of the effect and so the true effect must be bigger than what is reported in the paper. This is not true, not in general. Here's a simple example to show you why but it's not the only mechanism that will produce this. Suppose we're interested in estimating the causal influence of parent income on child income. However, parent income is not really observed. Instead we have a proxy of it and that proxy comes from the child's recall of what their income of their parents was like when their parents were the same age. This parent income variable, which I've written here as P star, is a function of both the true parent income shown there with the dash circle around it to indicate that it's unobserved and some error, e sub p, on this graph and we can add it to our DAGs like anything else. And to add a little bit more complexity here, but realistic complexity, the child's income itself biases recall and influences the error such that they tend to recall their parents' income as more similar to their own. And in this case where we have some variable that's measured after its causal effect these kinds of errors are not rare, or at least they're thought not to be rare. What do they do? Well, they can do lots of things, but they always induce some kind of bias in our estimate of the causal effect. So let's look at this very simple code example here. This is like the other code examples in previous lectures. I'm going to take you through the little bits of the code and show you how each bit corresponds to the DAG on the right. The first thing we do is we simulate parents' income. It has no parents of its own, the variable. So we simulate it first. Then we can simulate the causal effect of parents' income on child income. And just for the sake of this example, I've made the causal effect zero. You'll see in the code on the left I'm multiplying the parents' income by zero so that there's no causal association at all between the child's income and the parent's income. It's not realistic. It's just a provocative example. Then we simulate measurement, and that's the rest of the graph. And this is what I'm doing is creating a mixture of 80% of the parent's income and 20% of the child's income, and that's the mean of p star. If you wanted to calculate e sub p, remember it's just the difference between the parent's income p and p star. And then we can run the model. This is an ordinary linear regression programmed in ULAM, and we get an estimate. And what you see is that the slope coefficient b here is all the probability masses above zero even though the true causal effect is zero in the simulation. This is not a complicated example. This sort of stuff is typical, and it's meant to highlight that even in very simple data analysis problems these sorts of measurement processes can lead us astray. In this particular example, the bias depends upon the size of the original causal effect. So if the causal effect is zero, it biases us up. But if it's large, let's change the simulation to make the causal effect so that the actual coefficient is 0.75. Now the estimate is below that. As you can see, I've updated the posterior distribution plot in the lower right again. And the vertical dashed line is the true effect, at 0.75. And you'll see that we've gotten nowhere near it, and that's the consequence of the measurement error. So what's a general way to do this? You could probably intuit from the previous example that what we're going to do is try to add the measurement process to our generative models, whether those generative models are the sort of heuristic DAG types or much more specific simulations in order to understand measurement and deal with it in a transparent and justifiable way we need to model it. And that's what we're going to start to do. And in the rest of this lecture, I'm going to give you just two examples of ordinary sorts of measurement error problems and then at the very end, I'll mention the wider horizons of ways that the statistical community has tried to deal with measurement error in principled ways. We're going to return to this marriage divorce, age of marriage example from the first half of the course. So I don't have to reintroduce this data set. There are a couple of issues that arise from the fact that all of the variables of interest here as the divorce rate, the marriage rate and the median age of marriage in each state are measured with error. They're measured with error because the data were collected in a finite time window and only so many marriages and divorces occur within this time window. And this means that we don't know exactly what the long run expected rate is in each place. Of course, those rates may also be changing, but we can leave that aside and recognize that any finite amount of data we get an imperfect estimate that we have updated our prior from. So uncertainty remains about each of these things, these averages. Remember, averages are never observed. Rates are never observed. They must be estimated and so typically they always have uncertainty. So measurement error sometimes can be ignored. For example, if every entity in your model has the same amount of measurement error, then it all gets absorbed in the sigma. But there are lots of cases where that's not true. We're going to think about two here. The first is when there's imbalance in the measurement error. As I say, imbalance in evidence in this case. And in this data set, there's really strong imbalance. The states have much better estimates than others. And then the second is that measurement error can be related to other variables in the graph. And then as in the income example we started with, you have a potential for confounding. So let's look again at the divorce and marriage data. But now let's add the errors in the data frame. I've provided standard errors for the divorce rate and the marriage rate. And I've plotted these together with the variables on the graph on the left of this slide. And you can see that there's a lot of variation in the size of these errors of the uncertainty in each point. There's a general correlation between the error in marriage rate and the error in divorce rate. But they're not the same thing either. What's driving this variation and uncertainty across states? Well, it's mostly, not exclusively, but mostly just the population size of the state. As you can see this on the right, I'm just showing you the divorce rate on the vertical with the standard error interval plotted there with it. And then the log population size of the state on the horizontal. Why does this arise? Well, because states with fewer people have fewer divorces and marriages every year. And so they provide less data. And so you'd need a longer time series of data to get the same precision of estimate as a large state like New York or California or Texas. So let's think generatively about this measurement error process and add it to the heuristic causal model. Well, let's start with just one variable at a time to keep it easy. And we'll start by taking account of the fact that the outcome variable divorce is not really observed. The divorce rate is not observed. Instead, we simply have some pale ghost of it. The D star here, which is the observed divorce variable. And it is a function both of the true divorce rate D, which we can't observe. And some measurement process which generates errors, different error for every state. Of course, the other variables also are not directly observed. And so this structure is mirrored for the other variables, making a quite complicated looking heuristic causal model. We're going to don't panic because we're just going to back up a bit in a moment and deal with one variable at a time. But for now, let's think conceptually about other issues. With what we've got on the screen right now, if the errors vary from state to state, that means if we fail to take into account the measurement error, then we will be giving undue weight to lousy data in some cases that may lead us astray. So that's already a problem. But as I showed you, it's extremely plausible that the errors are caused by influence by the population size in each state. And so in this case, we start to see that there's potentials for noncausal paths that are opened up when we start conditioning on the star variables, which are in each case a collider on the path thereon. Remember, we can't regress on the true variables in this graph. We have to regress on the observed ones. And so potentially we can get into trouble. Suppose, for example, that population size also influences divorce rate in some other direct way. That is, in small states, the marriage market seems really different for people, and they may be more or less likely to get divorced. The same applies for marriage. In that case, it's possible that you can get all sorts of backdoor and other noncausal paths that cause us difficulties. And in that case, we want to think very carefully about these things. You may intuit here we could condition on population. We might be able to also incorporate the measurement error itself into the graph and make it work. How are we going to develop a solution to something that looks this complicated? And what I want you to do is think back to the pancakes. Always trust the pancakes. And what I mean by that in this case is try not to think like a regression. Resist the urge to be clever, and instead think like a graph. What I'm going to call for this lecture, thinking like a graph. The problem with thinking like a regression is that when you think like a regression, the idea is that you've committed to a particular very narrow range of statistical models in which your job is to figure out which predictor variables to use and how to combine them on the right hand side of a linear model. And that is a very narrow part of statistics because it's a very narrow set of approximations for modeling natural systems. What we want to do instead is think like a graph by which I mean, how do we model the network of causes? And this could involve multiple simultaneous equations, not just one. And it takes direct inspiration from your causal model, whether it's heuristic like a DAG, or something much more algorithmic, like a structural causal model or a set of dynamic equations. So let's think like a graph. And that means we're going to break this thing up and think about it as being a collection of submodels, which are all taking place simultaneously. And we can build a statistical analysis from that that deals with measurement issues as best as the available information allows, but does it in a transparent and justifiable way? So I said I'd simplify again, and I will. So let's pretend we've observed A and M, the agent marriage and the marriage rate without error. Just pretend for the moment to keep it simple, but that the outcome variable divorce has not been observed. Instead, we've got this proxy delta star. And I want you to realize is that we've got a couple of submodels inside this causal graph. The first is the model for divorce, how the real unobserved divorce rates are produced. They're influenced according to this model by the marriage rate and the agent marriage. The other submodel is the model for the observations, the measurement model for D star. D star is a function of the true divorce rate D and the measurement process, which gives the errors ED in this example. Of course, there's a third submodel here, which we're not going to deal with just at this moment. We'll fold it in a little bit later in the lecture. And that's the model for M. M is produced in part by the agent marriage according to this graph. So this simple little tag here has three submodels, which implies three statistical models, but they are joint statistical models. They have implications for one another because they share parameters and data. So let's write those submodels. Again, just for now, we'll focus on just the red and blue subgraphs here and build up a statistical approach, and then we'll fold in additional complexity as we go. I'm doing it this way, not just so it's easier to understand, but because this is how you should work when you do your own projects. We know where we want to go and where we want to go is pretty complicated. So if we're going to successfully get there to have a real credible path to make it, we need to go one piece at a time. So we start with the red part, and this is a linear regression of the true divorce rate on A and M. Of course, we haven't observed the true divorce rate, so it's not clear how we're going to do this yet, but hang on, we'll get there. But this is the model that's implied by the graph, assuming you're happy with a linear regression. You don't have to be. This could be nonlinear. And then the measurement model in blue, the observed D star is just an additive combination of the true D in each state, D sub i, and the error for that particular state. And the errors, we have a bit of information from the statistical bureau that produced these estimates that the error on each state's divorce rate estimate is normally distributed with a mean of zero and a standard deviation that they have provided to us as data. And this is what we'll call S sub i. This is what is sometimes called the standard error of the measurement. We can rearrange that equation just by folding the error distribution in so that the distribution of the D star observations is normal with a mean of D sub i, that is the true value, and a standard deviation of S sub i, the reported standard error. Let's take a break. There are going to be a couple of breaks in this lecture because I think it's, even though it's not a computationally complicated lecture, it's conceptually complicated. So let's take a break already and please review the previous slides, make sure you're ready to keep going, but then really do take a break, take a walk, have a drink. And when you come back, I'll still be here. Before the break, we were looking at the sub models of this small causal network that contains measurement error and I asserted that we have these two sub models, the red one, which is the generative model of the divorce rates and the blue one, which is the measurement model for the observed divorce rates. Now let's do something statistical. We can put both of these models together in the same Markov chain and run them together and that's important to do because they share a symbol and that is they share the D sub i measurements that we haven't observed and we're going to make those measurements that aren't observed into parameters. Why can we do that? Because in Bayesian probability, unobserved variables are parameters. That's all they mean. And observed variables are data. That's all it means. And importantly, sometimes for a variable like a divorce rate, if it's measured with error, then the true value is unobserved and it's a parameter. If it's measured without error, then it's data. And in the same vector, sometimes some of the states will be observed with error and others without. You have a mixture of data and parameters and that's all okay. It's totally orthodox. So it's going to provide an automatic solution for us here if we resist the intuition that data and parameters are somehow fundamentally different things. Now to be clear, before I explain the code, of course when we do the calculations, data and parameters really are fundamentally different things. But the structure of the model, the equations on the right, happened before the sample does. That is the scientific structure of the model should be independent of the sample we get. And so whether some variable has been observed or not in the sample we have, that is what determines whether the variable is a parameter or data. In the model it's just a variable and when we make generative models, there's really no distinction between parameters and data. It's only after the sampling and when we build the statistical model that the distinction becomes important for the calculations. Okay. This will become clearer as we work through the examples today. But remember, it's all about think about the pancakes. You don't have to understand. You just have to follow the rules. And the meaning of the results are the rules of logic themselves, are the rules, the axioms of probability. Okay. The first model here is the observation model and this is just a regular old regression with some parameters inside of it and some data. So in this case, D stars and observed variables, the observed divorce rates. And we assign that a normal distribution where the mean is the unknown true divorce rate in each state. So that's a parameter. And then DSD are the reported standard errors in each case. And that's also data in this case. And then we have the submodel where we treat these unknown true divorce rates in another regression as an outcome in a regression. And it has the same structure as every other regression you've run, except now that these are unobserved values. But the model looks the same. And the rest of it's just a linear regression just as before. And we make this a vector of length n because there are n states of the true divorce rates that we haven't observed. And it turns out there's a lot of information in the data. These divorce rates are only observed with error. And there's a lot of information in the data that can be used to get more precise estimates of these through the regression relationship of divorce with the other variables. So what we end up inferring are 50 different true divorce rates. And each of them is inferred as a posterior distribution. That is, we don't know its precise example.  And the true value is not, in general, centered on the observed value. And I'll show you why. Here are the observed divorce rates plotted against the observed median age of marriage values for each state. Just as in the earlier examples in the course. And there was a regression relationship between these variables, right? There's a strong, potentially causal relationship between the median age of marriage in each state and its divorce rate negative relationship. And then what happens when we introduce to the model the fact that the divorce rates are measured with error and we run the measurement model at the same time as we run this regression. What happens is the divorce rate measurements shrink towards the regression line. And they shrink towards the regression line because of partial pooling. Because what we have done is we have created a varying effects model. We didn't know we were doing it. It was forced on us by the logic of the causal graph. But this is what has happened. And we have gotten partial pooling, which has shrunk the estimates towards the regression line for exactly the same reasons that you get partial pooling in the previous examples. So what I've done now is I've highlighted in red and pink the new estimates, including the new regression estimate there with the pink tilted bow tie. And then the raw data are still the black points. And you can see that a lot of points have moved quite a lot, especially the ones that are furthest from the regression line because that's how partial pooling works, right? The most extreme points that are the least consistent with the statistical inference are shrunk the most towards the mean. Okay. Oh, I wanted to say, sorry. I wanted to say the regression relationship itself has also changed a little bit, but only a little bit. There are lots of states that haven't moved very much and there's been a lot of movement on both sides. But you'll see that the pink bow tie part, which is the new regression relationship, is a little bit steeper than the previous, which is shown by those thin dashed contours. That's the previous regression relationship. Maybe if I run the animation again, it'll help give you an idea for how this is working. Yeah, and then you can see the regression relationship changes a little bit, not much. And again, it changed exactly as much as it should given the assumptions of the model and the data, as the probability theory has done the only thing it is allowed to do. It has followed the rules. Okay, let's fold in another piece of complexity. You know that there are other variables here that are measured with uncertainty, like the marriage rate and the marriage rate is symmetrical to the divorce rate. It's a predictor now. It's a cause, not an outcome, but it also has a measurement model that's structurally the same as the measurement model for divorce. Now we have more submodels, and we're going to take them all and put them into the statistical model just as before. To remind you, here are the two we've already dealt with. We have the measurement model for divorce in blue, and we have the generative model for divorce in red. And then we have two new models that we're going to add to this. We have the measurement model for the marriage rate in black on the left, and we have the generative model for marriage rate in cyan there on the bottom. And we're going to put all four of these submodels together in the same Markov chain now. So I'm going to walk through this. Don't panic one step at a time. At the top we have the measurement model for divorce. This is just repeating the structure from before, but I'll talk through the structure again, because I appreciate that it takes more than one example for these things to sink in. It's a paradoxical set of pancakes. So the observed divorce rates in each state have a normal distribution where the mean is the true value, and the standard deviation is the reported standard error. And then the unobserved true divorce rates in each state are a vector of parameters, one for each state, and the prior for this vector of parameters is literally a regression equation. It's a normal distribution with some mean and sigma where the mean is a linear model, and this is fine. So this looks exactly like a likelihood probability of data, because probabilistically it's the same, it's just that the outcome is unknown, but probability theory will still process it using all the legal rules of probability theory. And then this structure is mirrored now for the marriage rate variable. We have the observation model for marriage rate, which is again the observed marriage rates are normally distributed around their true values with some known standard error that comes from the population size and the survey process and so on. And then the unobserved true values of the marriage rate in each state, again it's like a linear regression, but the outcome is a vector of parameters instead, and this linear regression is the prior for the true value in each case. Okay, you run that Markov chain, it runs uneventfully, it samples quite efficiently, and one of the consequences now of having both a predictor variable and an outcome variable that are measured with uncertainty, flip back here and show you something I skipped over a bit until now. If you look at the model for D, there's a new bit, is that in the linear model for the true divorce values, we no longer have the observed marriage values, but the true ones, you see that in the line from you, it's alpha plus beta for agent marriage times the observed agent marriage plus a slope for marriage rate times the true marriage rates, which are not known, so that's a parameter. So what this model does, what the Markov chain does is it runs, is it averages over the uncertainty in the unknown marriage rates while estimating the relationship to the unknown divorce rates, so that's like a complicated thing to do and it would be for a human, but the computer does not find it any more challenging than any other probability theory problem, and this is a necessary, correct implication of probability theory and our causal assumptions, this is the way that we get these, as I said, if we're willing to relax enough and suppress our desire to be clever, then we can get essentially automatic solutions to seemingly incomprehensible problems like how to incorporate measurement error into our models. So back to this weird looking graph. The consequence of doing this, of having a regression where both the outcome and one of the predictors are actually parameters or are unknowns, is that you get partial pooling in multiple directions at the same time, and so now the marriage rates on the horizontal and the divorce rates on the vertical are both shrunk towards the regression relationship. The black points here are the original observed values and then the red points are the posterior means, in each case, for each state. And you'll see again the more extreme ones are shrunk the most, but there's a bit of a helter-skelter pattern of where the shrinkage goes, and that's because there's another variable here, the age of marriage, which has a strong relationship with both of these variables, and it's pulling sort of in a third dimension that I have not plotted. We want to look at the coefficients though, what happened to the regression relationship between divorce rate and the two explanatory variables, that is age of marriage and marriage rate. So I show you this on the left of this slide, in the upper right, we have the posterior distributions of the coefficient on age of marriage, and in gray, this is the posterior distribution we got long ago in the lecture I first introduced this data set in. If we ignore the measurement error, then you get a strong negative relationship between age of marriage and divorce. When we incorporate the measurement error, it makes it a little bit weaker actually, in this particular regression. It's still almost all the posterior mass is below zero, so we still be pretty confident that if this is a causal effect, it's a negative one, and still pretty substantial. There's been a bigger change for the coefficient for marriage rate, and you look at the lower right. So now the coefficient on marriage rate, and this is the one, remember, where we just incorporated some uncertainty for it. When we ignored the error, the posterior distribution straddled zero, and it was reasonably narrow around it. Now when we add the error, it gets wider, which maybe doesn't surprise you if you have less information about a variable than a wider range of causal effects are consistent, but it has shifted upwards as well. So it isn't just that it's gotten only wider, and the mean has stayed in the same place, but it's actually become such that most of the probability masses above zero now. Why did this happen? Well, as always in applied statistics, if you understand your context well enough, you can understand why probability theory produced the results it did in that particular case. And in this case, when we include error on the marriage rate, that ends up down-weighting some of the states that had particularly unreliable and misleading estimates, according to the model in these data, and that is what produced the change so that there's now more evidence of a positive relationship between marriage rate, even though we included uncertainty on the variable. But this is a good example, say, in other contexts, the opposite could happen or nothing could happen when you include a measurement error. When you add measurement error to a model, it can either hurt or help your analysis from the perspective of the results you're after. Either way, it's the only honest option is to do so. Okay, I'd actually at this point like to take another break. Again, the computational details here aren't really new, but conceptually this is wild new territory. So please take a scan back to the previous section, maybe all the way back to the beginning of the lecture, make sure you've got the key concepts in order, then take a walk, and when you come back, I will be here. Okay, welcome back. Let's start the final example of this lecture, another measurement error example, another data set. This data set comes from Northern Namibia, a place called the Kaukefeldt, and this is a very arid landscape with more livestock than people. The people we're going to be interested in are the Himba. The Himba are a successful group of Bantu agro-pastoralists who have a really interesting kinship system and family system from an anthropological perspective. It's a very small number of people for a very big area, only 50,000 people in what is almost 50,000 square kilometers of area. And their family system has something called bilineal descent. If you'll tolerate this for a moment, I am an anthropologist and these things I think are really important to understanding human societies, so please just bear with me while I explain what this means and why it's important to understanding the data we're going to look at. Bilineal descent is very rare in human societies, but it's also not unheard of. It's found many places. It means that people trace their descent both through the male and female line at the same time. They keep track of who their descendants were through their mom and who their descendants were through their father. And they get different rights and privileges through both sides. So in the case of the Himba, wealth is passed through the mom and this is called matrilineal inheritance. And so their access to livestock and material resources comes through who their mom was. So for example, young men receive inheritance from their mother's brothers, not from their fathers. However, they receive status through their father, particularly whereas it's related to religious rituals and rights. And they're also patrolocal. So women move to their husband's family location when they get married. Polygyny is common in the Himba as it is and for many pastoralists in Africa, meaning that men typically by the time they're a senior have multiple wives at the same time that live in large cooperative households together. The Himba also have a system which is rare, but again, not unheard of of what we'd call open marriages in Europe, which is that it is normative and indeed expected that both men and women will have romantic and sexual relationships outside of their marriages. And so on the right of this slide, I'm showing you just some data for the contemporary Himba. This is data collected by Professor Brooke Shelza. You see LA that in young people, middle-aged people and people over the age of 45, middle-aged people, both men and women report majorities of both men and women report having extramarital relationships. And this is totally normative in the Himba. So the question is, what does this do to the structure of families? Right? How did they work? The social norms among the Himba are that the social father, that is the man that is who is married to the woman, provides for all of her kids no matter who their fathers are. And this is the norm and it's accepted. Westerners often have trouble accepting that this could be true. And so one of the things that this has led to is an attempt to actually do paternity testing among the Himba. The Himba don't want this, they don't care, but they'll tolerate it. It's the Western scientists who want to know what is the actual rate of what's called extra-pair paternity among children in the Himba. So this is our estimate. What is the proportion of children who are fathered by extra-pair men in these marriages? And remember, this is not cuckoldry because it's culturally sanctioned in the Himba, it's okay. It's expected and lots of social fathers provide for kids that are their biological kids. It's just their job. But we're going to try to estimate the rate of it using genetic paternity tests. The thing about these tests though is that they're not 100% accurate and in this particular rate, even though the geneticists used the latest fanciest ways, genomic techniques to do the paternity testing, there's about a 5% false positive rate for extra-pair paternity. That is to say about 5% of the time a child will be assessed by the protocol to not be the social father's child, even though he really is. And this is an example of what we call in statistics misclassification. It's a kind of measurement error where the variable is discreet. You have a categorical variable and you end up misclassifying it. So how do we include misclassification in a statistical model? This is a very common kind of measurement error. So I wanted to show you an example of that as well. And the code machinery, the way you make the golem to do this, is very different than how you do it for continuous measurement error. So hang on. I'll walk you through it. So of course there's a DAG. We won't do too much work with this DAG, but I wanted to give you an idea again of the structure we're talking about here. The idea is that there's some outcome variable X for the extra-pair paternity. This is a 0-1 outcome variable.  And that child has a mother that you observe there on the right for M. And a social father, which is the mother's socially-recognized husband there in the lower left, the F. And these two individuals also form a dyad. This is like a social network. And this dyad is TMF. And there is divorce and remarriage in the Himba, like in most human societies. And so women and men can be in multiple marriage dyads over their lifetime. And all of these things can have an influence on extra-pair paternity through the quality of the relationship or the time they've been together or any number of other things. And what we're positing here is that the X is not observed directly. It's an unobserved variable. Instead, we get its pale reflection, X star, which is influenced both by the true value of X and some measurement error. And we're going to make a model as before. Now, the general structure with the submodels and stuff is the same here as it was, or at least sufficiently the same here as it was before the break in the marriage example. The action here is going to be in how we have to code this up. A discrete error is different. So bear with me. The first submodel is the generative model at the top of the slide. And I don't think there are any surprises here. I'm going to include in this one just the mom as a varying effect so that each mom may have a different rate of extra-pair paternity among her kids. And that may be because she's less close or closer to her boyfriend than she is to her husband. And then we're going to have dyad level effects as well represented by the delta here. And these are standard varying effects as in the previous lectures. Nothing really surprising going on. We do need to use non-centered coding for these, but you're a pro at that by now. The measurement model at the bottom is the new bit. So, and this is going to take some explaining. So let's focus on that. To make the measurement model work, what we need to be able to say is how each of the possible values of X star can be produced through the measurement process. And I've written two equations to express that. And maybe you already intuit why they have the structure they do, but if you're like me, you need to remind yourself every time you do one of these models why it needs to have this structure. And that's important. Remember, trust the axioms. Avoid being clever. So it's nice with these sorts of problems to make a probability tree where there are branching possibilities. And then we can count up the possibilities and get the equations we need to express the probabilities of each event. So the first thing that happens when a measurement is generated is the actual causal process. And so I'm showing you in this first little probability fork on the screen here in the middle of this slide. So there are two possible true values for the X variable. Either it equals one or it equals zero. When it equals one, the child is an extra pair of eternity. That means one of the boyfriends is the father, is the biological father. The social father will still care for this child among the himba. Or X sub i equals zero, in which case the social father is also the biological father. And these events happen inside the model with probabilities p sub i and one minus p sub i. This p sub i will be our probability from the generative model of an extra pair of paternity. And then if the true value is actually zero, there's a chance of a false positive. And the false positive probability is going to be represented by the symbol f here. And it's about 5%, about 0.05 for this particular example. And then we produce X star finally at the bottom down here. So in the case that X sub i equals one, there's no possibility of measurement error in this example. The idea is that there are not false negatives, but there are false positives, and that generates this tree. So now we can use this tree to justify the equations at the top. Let's start with the first one, the probability that X star i equals one. Well, there are two ways that could happen. Either the true value X i equals one, in which case we will always observe a one. And that happens p sub i at the time or, and remember whenever you say or in probability theory, you add, you put a plus in, so p sub i or one minus p times f. And that's the other possibility, the other way to go down this probability tree to get to X star equals one. And then for X star equals zero, the only way to reach that is for there to actually be a zero and to not have a false positive. So it is one minus p sub i times one minus f going down the right branch twice. So we take these probability expressions, which again are just expressions of the rules of probability theory, nothing really exotic here. Just apply to this particular case, and we can program them into a new law model. And this is where the golem gets grumpy. We have to do this in a particular way. And I want to take a little bit of time in this example to focus on the code, which is not something I've done a lot in this class. But I want to do that because I want to emphasize that for these sorts of problems, it often pays to focus on the code a bit because there are different ways to do these calculations and some ways are better than others. So let's start with something that I hope is fairly transparent. So in this particular case, we can express these two probability expressions rather directly in the ULAM code. And the trick for doing this in ULAM is you can put this little pipe next to an outcome variable and say that there's a probability expression that applies only to particular values of it. So here we have x pipe x equals 1, which means the distribution of x, the probability of x conditional on x equaling 1 is, and then I have this custom thing which just lets you directly inject stand code into the model. And so this is some raw probability function that we're going to write. And then we just write the logarithm of the expression on the right. That is p plus 1 minus pf. That's the logarithm because stand does all of its math on the log scale. And that's the way statistics is done nearly always. And the reason is because that's more precise. I'll talk a little bit more about this in a moment. And then for x equals 0, the same sort of line, but then the corresponding function, the log of 1 minus p times 1 minus f. Okay, this model works and it works fine and we'll look at the results in a little bit. I want to spend the next several slides talking about other ways to code this that are better because if you get into this business and you start making your own misclassification models or other models that have these sorts of expressions in them, and there are lots, this way of coding it can be very bad because it can lead to numerical problems. So there's a better way to do this and I want to slide you into it slowly. The basic problem is that the way computers do math is crazy. So to speak casually. That is, math in the computer is a different system of constructing the real numbers than the way mathematics actually constructs it and the way you learned in secondary school. That is, computers use something called floating-point arithmetic. Computers can't really represent an infinite number of values or an infinity of infinities and other crazy things that happen in actual mathematics. But they use this system, this very clever system called floating-point arithmetic to approximate all that. And for most calculations, most of the time you don't have to pay attention to the differences between floating-point and real math, but sometimes you do. And in particular, when you're doing probability calculations, those differences can cause some real grief. And that's because probability calculations, because they're tightly bounded between zero and one, have a tendency to underflow to zero. That is, if a probability gets really small, close to zero, the computers will often tend to round it to exactly zero and that's catastrophic with a probability calculation. So imagine, in a very large data set, any particular outcome is extremely unlikely. Even if you know the true process that produces them, think about the garden of forking paths from early in the course. And so probabilities for any large data set are often very small, but they're not zero. And it's important to preserve that fact that they're not zero. Okay, the other problem is on the other end, is that if probabilities get close to one, which doesn't happen as often, but it can happen, they may round to one.  Often then the model won't even run, or worse yet, it'll run and you'll get the wrong answer. The solution to this is to do every step of the arithmetic on the log scale because these underflow and overthrow problems are much less likely on that scale. And there are, so that's why we take the logarithms already in the previous code, but we can also work with all of the probabilities on the log scale to begin with and not even work on the raw probability scale at all.  And they look a bit odd. They're ancient incomprehensible weapons. These things like log-sung-exp and log-1-m and log-1-m-exp. But they're indispensable if you do this business for very long and you get to know them and then become your friends. So let me show you an example of mixing in some of these ancient friends into our code and we're going to make a better version of the extra pair paternity model. So, same probability expressions at the top here. New code. And I'm going to focus on each of these lines and explain what we've done. So I've re-expressed this p plus 1 minus p f line is a much longer bit of code now that has two weird functions in it. Log-sung-exp and log-1-m. And what are these doing? Well, notice first of all that inside this log-sung-exp thing there are two arguments. There are two terms and these are the two terms in the expression at the top and the first one is p, but it's the logarithm of p, obviously, as it is here. And the second one is this log-1-mp plus log-f. And this is the logarithm of the second term. And log-1-m is a function that returns the logarithm of 1 minus what is inside of it. I'll say that again. Log-1-m is a function that returns the logarithm of 1 minus whatever is inside of it. And this function is nice because it does that operation, that calculation in a way that is much less likely to produce catastrophic underflow or overflow, in this case, is the danger, right? If p is a very small number and you do 1 minus it, it might be 1 and that would be very bad. So this is a nice little tool. It's one of these friends that we use all the time in this business. And then we add the log of f. Why do we add? Because on the log-scale multiplication is addition. And then what does log-sum-xp do? This is a workhorse tool in this business. If you've got a long probability expression where these different products are added together because they're or's, remember, in probability theory when you say or, you add. What you want to do for numerical stability is compute the log of each of the terms that are separated by pluses. And then combine them all using log-sum-xp. What is log-sum-xp? Well, it returns the log of the sum of the exponents of each thing inside of it, which means if we have log probabilities inside of this thing, which we do, it gives the sum of those probabilities because if we exponentiate each of those terms, it takes it off the log-scale onto the probability scale again, then they're added and that does the calculation that's at the top of the slide. And then we take the log of the whole thing, which is what we want to add to the target, which gives us the surface that the Hamiltonian simulation is going to cruise around on. I know this is weird, but there's really no avoiding this stuff. And after you work with a project that uses this, it seems a lot less weird, actually. But numerically, it's much, much more stable. And there are many projects which you just can't successfully complete unless you're willing to program the model this way. The other term for x equals zero, same logic, but it's a simpler expression here. We just have one term on the log scale. It is log 1mp, that is the log of 1 minus p, plus the log 1m of f, right? The log of 1 minus f. And this model will run too, and it gives you the same answer as the previous one because in this example you can get away with being sloppy. But we want to show you the right way to do it in case you need it. We can go one step further. Apologies to show you that we can gradually take everything off the raw probability scale and just do all the calculations from the very beginning on the log scale. That often helps. So another thing I've done here is we've taken the loget part of this model itself and just do it on the log scale originally. With all the calculations for the x's, we don't need p, we need log of p, so why are we computing p? Let's compute log of p. So this is what I've done now. I've changed the linear model so that it is the log of p. And then the inverse link now is the log inverse loget, which is a function that Stan provides. It's like inverse loget, but it doesn't go all the way to the probability scale. So it's more numerically stable than going to the probability scale and then taking the log. And then it's just a linear model inside of it as before, nothing too surprising there. And then in the expressions, the custom expressions for x conditional and x equals 1 and x conditional and x equals 0, I'm now including log p instead of p. Yeah, and then so log 1 minus has now been changed to log 1 minus x, which means we're going to get the logarithm of 1 minus the exponent of what's inside of it. And maybe this sounds like this is a lot of extra operations, but actually it's not. So this function does this calculation in a way that uses diffused operations possible and it is most numerically stable. So it's better to do this than the other options that I've showed you in this lecture. Okay, all three of these different varieties of model will produce almost identical posterior distributions because, again, in this example, you don't get underflow or overflow, but sometimes you do, so it's good to know how to deal with that in case it happens to you. So here are the posterior distributions for the misclassification model shown in red and a version of it that ignores error, which I haven't showed you, but I'm confident you could code that version on your own. The code for it is in the script for this week. And the thing that we're estimating here is the probability of extra pair paternity. This is per child. And this is clustered by women and dyads. And you'll see that it's around 50% a little bit below on average, but that there's a wide range. So in this particular sample of HIMBA women can range anywhere between about 0.3 up to about 0.7 in the high density region of the posterior. And you'll see that the effect of incorporating misclassification has been to reduce the estimate a little bit. So it's important that we want to get the right answer and we want to do it in a transparent and justified way. This is very high compared to comparable estimates in Europe, by the way, where they're below 5% always. But this is socially sanctioned in the HIMBA. We were expecting this. At least the anthropologists were maybe surprising to others. Okay, this has been a lot. This is a conceptually deep lecture. I appreciate that. It would be a good time again to review and look at the bits that might remain confusing and run the examples and play with them a bit to help fold in some of the understanding. Their measurement problems are extremely common in real research. And there are lots of related problems that are about measurement, which may not look exactly like the examples in this lecture. So in closing here, I just want to mention some of them. Lots of statistical tasks involve ratings and assessments. So you have judges, which are scoring wines or students or dancers or teachers, and you have tests of students or job applicants or any number of other things. And judges and tests are noisy instruments. They don't exactly measure the thing of interest. The thing of interest typically cannot really be observed, whether it's some talent or knowledge or how much someone has, how much potential somebody has, or how good the wine will be for some generalized audience that might consume it. There's a family of statistical models that are really just deployed industrially now. They're successful workhorse sorts of devices, a fleet of deployed golems. They're known as item response theory, which is actually a special case of some broad area known as factor analysis. And these models all are measurement models explicitly. They posit that the thing we really want to know is unobserved, and they try to estimate how different measurements related to it give us information about it. So they're simultaneously trying to construct a model of the measurements themselves so that they can get better measurements of the thing of interest. There are also models called hurdle models, where in a hurdle model there's something you're trying to measure, but if it isn't sufficiently present in high enough concentration, then you can't detect it at all. But you know that doesn't mean it's not there, so that there's a kind of noise for small values that is zeros may not really be zeros in hurdle models. And typically in these sorts of models, you need to model the zeros and the non-zeros simultaneously using separate distributions, so they're measurement models. Occupancy models are really workhorse models in ecology, in parts of ecology, but also in other industries. Often it's true that just because you didn't detect something, that's not a good reason to assume it isn't there. And so we can approach this in a generative statistical way, and there's a big family of models known as occupancy models, which do that. Okay, this has been Lecture 17. We're in Week 9 of Statistical Rethinking 2022. In the next lecture, we're going to extend the concepts here into missing data. Missing data is a particular kind of measurement error, if you will, and so we'll carry on and build on what we've learned in this lecture to see how to deal with that as well. And I'll see you there.


Welcome traders to the weekly market outlook for a week commencing the 17th of May with me, Patrick Munley. The second quarter of 2021 was always going to be a tricky period for asset markets, where inflation was set to spike and the Fed's dovish policy would come into question. So far, markets have coped reasonably well with the April US inflation pushing above 4%, and the DXY, surprisingly to some, is barely 1% above the loads of the year. On paper, the weak hedge should not interfere with this benign trend. The US data calendar is light, just April housing starts and new home sales, and the highlight will probably be Wednesday's release of FOMC, minutes from the 28th of April meeting. Perhaps the key takeaway from Powell's press conference that day were the words, now is not the time to talk tapering. With that in mind, expect the markets to absorb in their stride any suggestions that a few participants were a little less dovish. The weak hedge will also see China release April retail sales and industrial production. Markets will also be watching whether any Chinese official concern over commodity increases has any follow on through selling in that complex. Traders should also keep an eye on US big tech shares. These have been suffering at the hands of higher inflation. It could be a better week for this sector, given the US price story should be quieter. So from a technical perspective, we are still looking at the potential for this way for high in place in the dollar. And so we're looking now for a breach of last week's lows at $89.94 to take us into the $89.65 through there into the prior lows $89.26. Expect the potential for a small bounce there, but ultimately now I'm looking for a test of monthly range support down to $88.55 before we see any more meaningful correction. The only risk to that is that we get a sharp reverse along Monday. That could take us up into the monthly pivot for a test before we see the next leg lower. But if we don't see these any buyers early in the week, then I anticipate a slow grind lower. In Eurozone, the Euro dollar, actually whether the first batch of strong US days are relatively well. Keeping Euro supported is a couple of factors. Firstly, the Fed committed to looking through the inflation spike and keeping US rates very negative. And secondly, confidence growing in the Eurozone recovery and traders starting to ask questions of the ECB whether Euro real rates are right to be as equally negative. In other words, with the ECB have less tolerance of higher inflation than the Fed. Contributing to that debate in the week ahead will be a variety of speeches from ECB big hitters such as Lagarde and Lane. We'll also see the first revision to first quarter Eurozone GDP seen at minus 0.6% quarter over quarter. More important will be the first look at flash BMI's for May coming Friday, expected to stay strong as economy starts reopen after third wave lockdowns. German elections may drift into the markets radar this week when candidates to replace Angela Merkel debate on Thursday. Latest opinion polls show the Greens still with a slight lead over the CD UCSU making the case for a green representation in any new coalition government. Green policies of slightly looser fiscal settings and greater European integration are seen as Euro positive. From a technical perspective, Euro dollar held the trendline test at 1247. Nice outside reversal day on Friday. With all momentum looking bullish at the moment, look for follow through through Friday's highs to initially test the 12240. You may see a bit of back and feeling there, but ultimately now I look for a test of the sending trendline resistance up towards 123. Again, similar to the dollar story, only a sharp reversal on Monday really would see us pull back to test the monthly pivot before extending higher. In terms of the yen, once again, it was one of the pairs to be impacted the most by the US CPI print. Most understandably, are convinced that US rates are too low at this stage in cycle and that it's only a matter of time for US 10 year yields pushed towards 1.92% area. Dust expectations of building that the dollar yen will exit its 108 to 111 range to the top side. This view does require a jump in US real rates, however, and so far there has been little sign of the Fed preparing to play ball by offering a less dovish setting. That's why not as bullish as some really in terms of the dollar yen. We'll talk about the technicals in a minute. Away from the US calendar, we'll get our first look at first quarter 21 Japanese GDP this week. This is expected at minus 1.2% quarter over a quarter. BOJ has actually been revising up its growth estimates recently, so GDP data should provide some insights on whether they were right to do so. We'll also see the April trade balance this week and April CPI, expected still at minus 0.2% year over here on the core measure. We're also hearing a little more about traders wanting to rotate into Japanese equities, especially after the recent dip. Let's see how resilient foreign interest is when the weekly Ministry of Finance portfolio transaction data is released on Thursday. So from a technical perspective, once we hold the swing low here at 108.34, we're looking for an equality objective at 110.51. Really only a loss of the trend line support down to 108.60 would concern this bullish view, opening the door for a deeper corrective move to test towards the monthly range support at 106.60. Cable took out 140, and even the material upside surprise to the US April CPI was not enough to bring the cross below the psychological level. See the impact of the recent US CPI spike on cable as a one-off and temporary and look for further trend higher. Domestically, although the spread of the Indian COVID variants is rising concern, this is so far being linked only to specific regions. Importantly, the vaccine seems to be working against the variants. As a result, the general reopening story should therefore go ahead and the improving UK economic data should continue to support sterling. The UK data points this week should be positive and help GDP too. On Tuesday, look for another decline in unemployment. Wednesday's April CPI should age higher to 1.5% year over year and is to exceed 2% later in the year. On Friday, April regal tail sales should rise, linked to the reopening of shops in April, and May PMI should be encouraging the economic outlook is improving. So from a technical perspective, once we hold 140, we now look to retest the prior cycle highs here at 142.40. Through there we can start to think about the monthly R3 at 143.31 and then on to the yearly R1 at 144.30. At this juncture, any pullbacks into the ascending trendline support here at 139.17 should be well supported and look for bullish reversal patterns to add to long positions looking for new highs in this cycle. Finally, in Australia, so far a supporting factor for the Aussie has rapidly turned into a negative one. Iron ore prices experience a fierce sell-off late in the week after China took steps to control the surge in commodity prices. On Friday, Tangxian City banned steel makers from fabricating or spreading price high confirmation. We should now see these levels of iron ore prices look unsustainable of late and a resilience in Chinese demand inflates them. Now any signs that demand could shrink could set to see a corrective move in iron ore prices. The iron ore market is the one to watch next week for the Aussie, although the April jobs report in Australia will also be in focus. The recovery and employment should have continued in April, although likely at a lighter pace. Any market impact of the release may be relatively contained, considering any hawkish term by the result back of Australia is unlikely to be imminent, considering weak inflation. The minutes of May's RBA meeting should reiterate how low inflation continues to make a case for lower for longer. So from a technical perspective, held the monthly pivot at 76.90, a nice bullish reversal pattern there, so I look for a move through Friday's highs now to certainly retest this 78, 80, 79 zone and if we can continue to support there, we look for monthly range resistance 79.60 and then on to the price cycle highs above 80. Really at this stage, only a loss of the 76.80 would concern the bullish view, setting a move to test monthly range support to 76.10. So that concludes the weekly market outlook for week commencing 17th of May. As always traders, I wish you all the best for the week ahead. Thanks very much. Goodbye.


What's going on in the family? Welcome back to another video. It's your girl Janice. If you guys are new to the channel Make sure you hit the subscribe button and join the family today I am going to be pranking Isaiah by not telling him that I love him back. Now Isaiah is supposed to go and play basketball I'm gonna be chilling and when he says I love you when he leaves like he always does because you know when they're significant Oh, they tells you that they love you when they're about to leave you always have to say it back That's just that's just what you have to do. So guys when I say I like you too He is going to not like the back. So guys if you are ready for today's video Don't forget to smash that like button comment down below team Janice and let's get this prank started I didn't say I like you. I know I said I love you. I heard you Okay, so okay, so I said I like you too. What's the problem?  I said I love you I know that but I'm saying I like you What what it's not what you're supposed to say you're supposed to say I love you too. It's the same thing No, it's not the same thing. No, it doesn't know it's not to me It's so if you see someone you like that doesn't mean you love them, um, but you So, yeah, no, we're past that phase. What do you mean? What phase that's the beginning phase We passed that phase seven years ago. It's I love you now. Where's this?  What do you mean? I'm not mad. I'm fine. So why are you saying I like you? I said I love you Why are you not saying it back? I didn't think this was like a big deal. I literally am just saying how I feel. That's it So you don't love me? I do but okay, so say it. Why are you saying I like you? Because I just wanted to say I like you too.   No, you don't you don't you never say that I always say that.  Are you giving me like hints that you're upset? I'm not upset. I'm telling you I'm 100% fine. I'm happy. I'm good. Like I told you to have fun I just want you to go and have fun and enjoy your time. It's not that big of a deal Like I said, I literally just say I like you too. Like it's not that big of a deal I think you're making it bigger than what it actually is. No, I think you're trying to hit that something No, I think that you're just reaching. No, I'm not reaching.  Is that what it is? It'd be nice, but no. Oh, it'd be nice. So is that what you want me to do? Babe, please. I'm gonna go play ball. Okay. Have fun. Okay. I love you. I like you too What you're supposed to say that's not what a girlfriend says to a boy for back after he says I love you I think you're doing the most I know you're doing the most it could all be It could all be so simple I love you too. That's it But I don't want to say that Okay, do me a favor. Let's let's play. Let's have a little role-play here. Say I love you. Just say I love you Why? Just say it. Just say I love you. I love you.  You see how it doesn't make sense. It's weird.  I'm not lying. I'm serious.  You're not gonna feel the same way.  No, I will understand. Okay It's just a different way of expressing how you feel like does not mean love and vice versa. Okay So I love you. What is your point?  Are you not understanding what I'm saying? Do you want me to say what you're saying back? Is that what it is? Yes But that's like forcing me to say something I don't want to say, you know Why don't you want to say you say every single day you say every hour? Why are you not saying it out? I think you're upset because I'm gonna play ball. Babe, I'm not mad.  So say it back Oh my goodness. Why are you doing this whole thing? Just why are you? You're the one like Just say it back. Just say it back. It's easy. It's three words. I love that's all you gotta say Babe, you could have left a long time ago. I could have but you're not letting me.  Why just say it back. Tell me how you feel. Why are you upset? Bro, I just told you it doesn't make sense. Why are you saying that? I didn't do anything for you to say that Babe, I'm not saying anything bad. I'm just saying I like you We're past that stage. It's I love you now. No It's like saying I love you and love you if you don't say the I And you just say love you it kind of is like all right, like there's no effort in that All right. No now that's kind of like oh, okay, I'm leaving. I love you Come on. Hello. Is that what you want me to say to you? I I'm leaving. I love you Okay, see you later Say you back. You're walking to the wall. Say it back Say what back? I love you later. I love you. See you later. No, say it back Say what back? All right.  Whoa The infinite fam how much you want me to say I love you back All right, infinite fam. So I clearly came with a banger for team jenice. I love you, babe I love you. I love you. I love you so much. I love you. I love you I love you too. I love you too. I love you more. Thank you. Thank you.  I know vlogmas is almost over But I hope huh weak sauce weak sauce your whole team is weak sauce and I realize I have white socks on I gotta go change that to black socks. Okay. Thank thank you for letting us all know that you have to change your socks All right guys, so it's time for today's post notification shout out today's post notification shout out goes out to life with chins Thank you so much for your love and support. Izan. I love you If you want to post notifications shout out all you got to do is like comment share and subscribe Don't forget to turn on those post notification bells to notify whenever we post a new video And with all that being said we will catch you in the next vlogmas video


Greetings, everyone, and welcome to Working Together on ThinkTech Hawaii, where we discuss the impact of change on workers, employers, and the economy. I'm your host, Cheryl Crozier-Garcia, and we invite you to join in the conversation. Please call us at<PHONE_NUMBER> with your questions and comments, or if you prefer, you may tweet us at thinktechhi. One of the simplest ways to see change in a community is to study its commercial districts. Here in Honolulu, the Jaguar dealership on Baratania Street is now a goodwill store. The Liberty House on Fort Street Mall became a Macy's before morphing into a Walmart. Remember Schumann carriage? Now it's Makani Kai Air, running commuter flights between Honolulu and Moloka'i, and its former location on the corner of P'ikoi and Baratania Streets is a safe way. Most of us who grew up in Hawaii remember the small family-run stores where we spent our allowances on crackseed, shave ice, and shredded cuttlefish. Sadly, most of our cakey won't have those experiences. Long-time, locally-owned businesses are closing, being replaced by large brick-and-mortar retailers, as well as by e-commerce enterprises. One of the largest electronic retailers, Amazon, recently acquired Whole Foods. While that was probably a good strategic move for Amazon, how will this affect shoppers, workers, and those who compete with what is becoming a real behemoth of a business? Joining me today to share her insights on this issue is Carol Mon Lee. She's the Executive Vice President and Chief Operating Officer. Welcome, Carol. Thank you, Carol. Nice to be here with you. And you know, before we get started on the real conversation, we need to introduce our super special secret guest, Minky. Yes, this is Minky Mon Lee, actually Minky, too. Minky, too? Yeah, she's part Maltese. Oh, how wonderful. Mm-hmm. She's cute. Is she shopped? Not yet. We haven't trained her to shop yet, but she consumes. Good.   And there have been some real changes over time in the way we approach acquiring the goods and services we need and then paying for them. What kinds of things have you experienced as a consumer and as a shopper that maybe are different today from the way they were, say, when you were younger? Younger. Oh, sure. And I'm a baby boomer just to give you a sense of where I fall in the spectrum. So of course, I was shopping long before there were computers or electronic devices of any kind. So of course I'm used to going to stores and actually touching or holding or checking the prices and then maybe using a calculator to figure out how much something costs. And price comparing in real time, right? And then buying and then maybe exchanging by returning something directly to the store. And of course all that's changed now. So I would say I haven't come along quickly like many of my younger friends and my children and my colleagues in terms of adjusting to the new way of buying. But certainly I do buy more things now online and I look online. I just had a recent experience. I was on a cruise ship and I downloaded a book on Amazon rather than buying the hard copy. And I read it online through my iPad. And I really enjoyed it because of course I was able to adjust the type, the font size. And then after I finished my book I picked up something else, a hard copy of a book, another book. I realized I can't expand the font and I felt boy that makes a big difference in being able to as I get older and wanting the font size to be bigger having that flexibility to do that with a book that you purchase online. Now of course I feel also that the downside is that I can't share the book that I purchased online through Amazon with someone else without, I don't know what you can do if you can do it at all. But there may be a way but I'm not sure what it is. And there are certainly copyright infringement issues if you were to just try to download it to someone else's device or something like that. Which is a lot different than maybe just here, read this. Of course. It's only someone a book. So I definitely noticed that as a recent adjustment that I've made. And of course buying clothes, a lot of my friends only buy their clothes online. But I find it, I prefer to touch and feel and then of course if it fits, I'll buy it and if it doesn't fit, I don't have to worry about returning something. How do you feel about the waste of packaging? I feel like there's so much packaging wastage, boxes and stuffing and the size of the boxes much bigger usually than the need for the object. And I just feel I don't want to contribute to that kind of environmental access. It does expand your carbon footprint sometimes if you purchase online and have things shipped to you unless you shop with a retailer that focuses specifically on using recycled materials etc. For example, just everything I have on today, I bought online. I have an app on my phone called Thread Up, which is a consignment shop slash thrift store type of operation. You can only buy via the app. They don't have a brick and mortar store, they have a warehouse. People send in their things and then they can either be taken on consignment where the person is paid after the garment is sold or they'll buy straight up and send you a check for whatever those things are. So everything came, but it was shipped, this was the interesting thing via USPS, the post office, in one of those flat rate boxes. And the box was small, they're not trying to wrap it up all nice with foam peanuts and stuff and wasting a lot of stuff like that. Now, gasoline probably, fuel costs associated with shipping. On the one hand may increase, but on the other hand those planes are coming to Honolulu anyway. And if they're not filled with my Thread Up box, they're going to be filled with other consumer items that we need.  Are you sure? Yes. Enough of the sizing? Okay. So typically when you buy, do you ever return? I usually don't have to. If I have certain brands that I know and I know what sizes I take in those brands and so that's what I tend to focus on. If I see something I like that I'm not familiar with the brand or the sizing, I may head into a store and look for that brand on the rack and try it on and see which size is appropriate. And then go home and order it online. And then go home and order it. Well what I do find is that using Thread Up, as well as using other kinds of, shall we say, secondary market type retailers, Plato's Closet and Savers, Goodwill, things like that, I never buy new anymore. Well I had another experience involving online shopping which was I had a young friend who was a tech person who helped me set up my second screen and realized I needed a new printer. So he was at my house, we were setting it up and okay I agree, I definitely need to buy a new printer. So he pulls up on his phone Best Buy. We look at several HP printers and he found one that was in my price range and did what I needed to do. So okay let's go ahead and order it. So I gave him my credit card, we ordered it, $109.00. And I could pick it up at the store locally so I didn't have to worry about being shipped and how long it would take. I could go pick it up the next day. So I go to Best Buy to go pick it up and the same printer there is $129.00. And I said, but I only paid $109.00 and they said, yeah, if you buy it online it's cheaper and you can still pick it up at the store or they could have sent it to me. I was very happily surprised by that kind of a situation. And I also know that there are some retailers who will also match whatever the price is online because typically prices online are cheaper, right, because they don't have the brick-and-mortar to have to overhead. But if they do have brick-and-mortar store and you go into the store and you show them the online price, they will match it. That's a nice development. Yeah, it really is. If the merchant is willing to take that step. Now a lot of times you should ask because they may not advertise that this is a policy that they have. But if you inquire about it they'll say, oh sure, we'll give you the discount. And of course now the news is that a lot of these brick-and-mortar stores are closing, right? We aren't hearing about how many, whatever it is, Walmart or Sears, big chains are shutting down many stores. So how do you feel about that in terms of you won't be able to go into those stores to actually try? Yeah, that's true. But a lot of the really big stores that have been closing, at least here in Hawaii for the last couple of years, Kmart, Sears, etc. I wasn't a big user of those particular merchants. Although I have to say that if I ever needed an appliance, Sears was the only place I'd go to. Of course, right. So I've got a house full of Kenmore because you knew the service was good, the product was fine, they'd install it for you, they'd deliver it, they'd take away the old stuff. They'd take away the old one, you can buy a relatively inexpensive warranty, they'll come fix it if it breaks. So for that, Sears, everything else, not so much. Well, but it also requires, if we're moving in that direction where there will be fewer and fewer brick-and-mortar stores, are there also equally almost a hundred percent access to the internet for most people? I mean, how do you do? That's a net neutrality issue.  If you have a cell phone, you can purchase additional technology that will allow you to access the internet. And you can walk into any public library. Or any Starbucks or any, and provided you've got a computer or a phone with computer access or a tablet or something, you can do your shopping there. Now, there are some security issues that come with that. If you put a credit card, pay with a credit card, yeah. And of course, the library, they do have computers, so you don't even have to have a computer. Right, right, and it's funny, you bring up the library because our library's going to go out of business. If we can download the books that we want, why walk into a library? Well, I used to sit on the Board of Education and used to be involved in public libraries. And actually, they've kind of pivoted in terms of what they do for the community, and they've become much more of a community resource center, not just books, but of course summer programs for students, after-school programs, adult classes, and of course, a place to buy and sell used books and magazines and sharing of all sorts of information. And then of course, the big one is internet access, and particularly on the neighbor islands, it becomes a huge way for the community to be able to go to one place and be able to have access to both the computers and the internet. Hold that thought, because we will be talking more about this right after we introduce our audience to some of the other awesome programming on Think Tech Hawaii. So I'm Cheryl Crozier-Garcia. This is Working Together, and we will be back in one minute. We have this crazy thing going on today. I was just walking by, and all these DJs and producers are set up all around the city. I just walked by, and I said, what's happening, guys? They told me they were making music. Working Together on Think Tech Hawaii. I'm Cheryl Crozier-Garcia here with Carol Monly and Minky talking about how shopping and e-commerce change the way we shop and the way we think about retail workers. And the issue of retail workers is something I think that doesn't get enough thought, because most of us, many of us, got our first paying jobs in some kind of retail-related business. If it wasn't cash-shearing at the local store, it was maybe a fast-food restaurant or something like that. And those are all retail-type positions. I still remember being taught in high school in the early Jurassic period how to count back change. You know, when you run the cash register, the total would come up, the person would give you their money, and you would have to count the change back to them. Today, not only can the average retail worker maybe not count back the change, but depending upon where you are, they don't even have to know the price. They can scan the items. And in some places, it is even as simple as pressing the button with the picture of the item. No kidding. Fast-food restaurant. Yeah, you want cheeseburger? Right. The person behind the counter will press the screen. The picture of the cheeseburger, and it will say cheeseburger. And so, in a way, the skill set that is required is so different. And I'm not sure, and since you mentioned that you had been affiliated with the DOE and the library system for a while, let's talk about some of those issues. How do we train our future generation coming up not only how to survive on some of these types of jobs as they're getting started in their working lives, but how do we train them to be good consumers of the vast variety of products and services that they have access to? So how do we do that? You know, I'm not sure because I'm not even a savvy consumer now. I don't consider myself a savvy consumer. I sure I leave money on the table all the time, right? I don't get the best price. My son can figure out what's cheaper than, you know, and he can shop. I just, whatever is easiest sometimes for me. So I don't know that I have the answer except that it seems that the younger you are, the more savvy you are in terms of course of online shopping, price comparing, knowing where to find the best deals, knowing some of these sites that I've never heard of. Yeah. And I find it interesting what people, because I teach college primarily. And so most of my students now are late millennials and quickly becoming Generation Z people. And what surprises me a lot is not only what they consider to be expensive or inexpensive, but what they would prefer to spend their money on. Very different. Yeah. I'll give you an example. When I was in college and I'd get my grant check or my scholarship check or whatever it was, the first things I bought or my textbooks and whatever school supplies I needed, my lab stuff, those kinds of things. And even if they were expensive, I sucked it up because I knew I needed those things for my education. Now, first of all, you're supposed to complain about the cost of textbooks. It's a rule. Really? Oh, of course. Okay. You're supposed to complain about textbooks. They are expensive. But a lot of them are online now. Yes. But even the online ones are sort of expensive too. And you would be amazed at what students will do to kind of work around the issues of the e-books, the loose leaf ones that are cheaper, these kinds of things. No, I know it. I'm appalled when I hear that a student tries to get through a course without ever buying the textbook. Yeah, there you go. I mean. That's one. Yeah. Here's another one that I find interesting. Do not come into me as a professor and tell me, gee, Dr. C, do you have an extra copy of the textbook? I can't afford to buy one.  I just, I cross my eyes and be like, are you kidding me right now? Was that a gift? No, I bought it. Okay, well maybe you should have bought a cheap one at Ross for $35 and then went out and got your textbook. Well, do you know whether, for instance, maybe it's high school or even younger than that junior high as part of the curriculum of learning how to cope with life, you know, the old days where you learned to balance a checkbook and boil water and, you know, do basic things. Are they including things like how to be a good consumer? There are life skills courses but I don't know how deeply they get into kind of the financial management issues and the consumer issues. Now you might get a class say in family nutrition where they will tell you how to prepare a balanced meal and how to do the, how to pick the best produce and stuff like that but I don't think they will go as far as to say, you know, oranges are good for you. They have a lot of vitamin C but there's more vitamin C in a such and such and they're cheaper or buy food in its own season and eat it in its own season. I don't know how far they go with those kinds of life skills. It can have a tremendous financial impact on the way a family structures its resources. So do you think that's something that should be focused on? That there should be more education for Gen Z? Gen Z, I think that there is a need for a lot more education. The trouble is that time is a finite resource and I also think that I would love to see kids taking classes in music and art and literature, getting time for PE every single day, these kinds of things. But if you've only got six and a half hours a day and less than 180 days in a school year to deliver content and then to assess how well a student masters that content, how do you, where do you cut? Right. More important, knowing that you need 8,000 milligrams of vitamin C a day or memorizing Hamlet soliloquy. So of course then parenting skills play an important role in educating your children to be a good consumer. I hope and it should but what do you do when the parents are working, you know each one works two jobs.  Meanwhile, oldest kid is maybe putting supper on the table for the younger siblings. Number two child is taking care of the laundry or whatever it is. When does the parenting happen? You know a lot of times kids have to figure it out on their own because there's no mom or dad to ask because mom and dad are at work. So let me ask you a question. So where do you see the future? We talked about Amazon Prime or Amazon purchasing Whole Foods. I know that was one of the original themes of the show. Right. So where do you see all this going? I mean Amazon is going to be the super store food and everything else in between. Well I think the Whole Foods purchase of Amazon's purchase of Whole Foods was a smart move for a couple of reasons. Number one they had been trying to crack the food market via shipping, home chef tight meals etc. And that didn't work. It didn't work. It doesn't work very well. Because if you're not home when the mailman shows up, you're kind of hosed food wise. The other thing is that having Whole Foods as a brick and mortar store would allow Amazon shoppers to say, yeah I'm going to buy all this stuff, I'll pick it up at customer service at the Whole Foods in Colomal. So Amazon is able then to use their supply chain to expand outreach to people who are not home to pick up the mail. So it ends up being good for Amazon, smart move. It will change the way we have to train people to work in the future. People say well we'll lose cashier jobs are going away. That's true. The box that gets shipped, somebody has to pack it and deliver it from point A to point B. So transportation industry type jobs are likely to increase as retail type customer service positions are decreasing. But there's still going to be room for people like me who want to go to the market and actually pick up a piece of fruit and not do shopping online. I hope so. Yeah. Okay. Particularly when we talk about food, the farm to table movement is forcing not only supermarkets but lots of other food retailers to examine the way they sell. There's a farmer's market down here on Fort Street Mall every Tuesday. I cannot imagine a time when you will call the farmer's market and say yo can you send me five pounds of dragon fruit and how are the peaches today. I'm not sure that that will ever happen. So there will always be opportunities I think for that human to human contact as far as as exchange of consideration but how it happens and how often it happens will change. So do you think it's a good thing? So in five years we have more online shopping, less brick and mortar. Do you think that's good for the economy, for our community, for our society? Well that depends on the alternative uses for those brick and mortar locations. I remember a conversation when Liberty House was closing and they didn't know if Macy's was coming but maybe they were etc. So we were chatting in one of my classes about okay so what do we do with that space and they said well what if we turned it into like a capsule hotel for folks that have housing insecurity. How many people could sleep you know with minimal changes to the infrastructure of that building and have a safe location to live to get a good night's sleep etc. So if the substitute uses for that space that is currently retail are good uses then they can certainly improve the way we live as a community. I mean at least I think so. And I'm not going to stop buying thread up because it's cheap. So then do you see Waikiki changing? Waikiki is changing sadly in my opinion because to be honest if you didn't see the signs written in Hawaiian you could just as easily be in South Beach or Puerto Vallarta or San Juan or any other place that has the kind of climate. And none of that stuff I mean I haven't been to Waikiki since I got married. When was that? Fourteen years. You haven't been to Waikiki since not in fourteen years? I haven't needed to. You don't have visitors from out of town who go to Waikiki? I give them my car keys. I see. See ya. But no I don't because there's really nothing in Waikiki that I can't get cheaper or faster someplace else. And Waikiki Beach is beautiful until you see Cayana Point or Kahana Bay or one of the other beaches where you're more likely to hear pigeon being spoken than what you would see in Waikiki. So I'll let the tourists have Waikiki. And then globally do you see online shopping that's the way the future even third world countries? How are they going to survive? Well, look at the Alibaba example in China. Alibaba is actually bigger than Amazon and they make money hand over fist in China by selling everything to everyone in an environment in a market where there are places where there aren't even paved roads. But everybody has a cell phone. But everybody has a cell phone. And I'm seeing a sign that says we're closing in one minute. So what quick advice would you give in one minute about hmm, oh I don't know, what kind of gift would you buy for Minky? Well Minky is low maintenance and as long as I give her food and shampoo and a lot of hugging and loving and she's a good dog. And hugs and love are free. Yes. That's what everybody should do, right? Yes. Let's challenge our audience today to do something like that. Your homework assignment between now and the next time I see you is to go out and hug and love on somebody that needs it. So we'll be back in two weeks for another episode of Working Together on Think Tech Hawaii. I'm Cheryl Crozier-Garcia. Thank you so much for joining us. We'll see you in two weeks. Bye.