Welcome back, in the previous lecture, we talked about how we could use models to become clearer thinkers. In this lecture, what we're gonna do is talk about how we can use models with data. And this is an important reason why people use models, in fact when you talk to scientists about why they use models whether they are social scientists or natural scientists. What they'll typically say is well we use models to take them to data, to basically use and understand data in better ways. What I am going to do is unpack that in several directions. I wanna give some specific reasons or ways in which people use models with data. Alright so the first one first real reason is just to understand some basic patterns in the data. So what do I need? Well you could look at data and it could just be a straight line, and nothing could change. So for you look at a system where there's not enough energy in the system we know that energy is neither lost nor gained so energy is a constant. And we have a model that explains why we see energy being a constant. Alternatively we can see something that's a straight line, and increasing line. When you're on a model that explains that. And then we also talked about how we can see patterns in data. So we could see things that go up and down slowly like this, like business cycles and we have models that tell us why we see these kinds of cyclic curves. We could have something that's much more spiking. We could have a model that explains that. So. Again we talked about how there this sort of hairball of data, this firehose of data. There's tons of data out there. That datas gonna have patterns to it. And what we can do is use models to understand why we see those particular patterns. Okay. In addition to the patterns, there's also the use of models to predict specific points. So suppose you are looking for a house and you see this house that's for sale and you're wondering, I wonder how much that house is gonna cost. Well, you can have a model that says okay, the price of the house depends on it's size. So here's sort of the size of the house in square feet. And here's the price. We just put dollar sign there for price. And maybe you get a linear model. And your linear model says basically for every, you know, additional square foot the price of the house goes $100 or $200 or something like that. Well then if this is your model, so on your model you've got a house that's got this many square feet it's 2,000 square feet, right, and you go up here and find the point it's $100 per square foot then you're model would predict that the house is $200,000 so. We can use just a simple model to make some sort of prediction about, just in ballpark, how much a particular house would cost, so this is, again, a common use of models to either construct a model and from that model, you predict a point value. Okay, third reason why we use models. It's not so much to predict the points, but to produce bounds. So suppose you're the economic advisor to the president, not a job you'd necessarily want, [laugh], but suppose you are. And the president comes to you and says, what's inflation gonna be next year or next month? Well, you know, inflation doesn't move that quickly. You might be able to say to the president, well, you know, I think it's gonna be 1.2%. And you might be pretty confident that it's 1.2%. But suppose the president says, you know what? I'm just doing some long range forecasts, so, what if, what's inflation gonna be ten years from now? Well, who knows what inflation is going to be ten years from now? So you may have some fairy sophisticated models, but they're not going to give you a point estimate. So, instead, what they might say is that I can tell you with pretty high probability that it's going to be between zero and three percent. So it gives you a range. Right? So what your model won't tell you exactly what's going to happen, cause there's too many contingencies out there, there's too much complexity, too much uncertainty. You can't say for sure, but your model might give you some bounds about what's going to happen, and that can be really useful for making policy decisions. Okay. Reason Four. Retrodiction. What do I mean by that? Well, you can use models with data to predict. Past. Now there's a couple reasons you might do this. One reason is you might not have data from the past, you might want to sort of use models to figure out, what do we think the past was like? And this is think, you know, geologists do this. You know, biologists do this, anthropologists do this, archaeologists do this. They use models and data to try and figure out, what do we think you know, temperature was like, how many animals do you think there were, what were these civilizations like, those sorts of things. If you have the data, then you can use models to see how good they are so you can actually retrodict data to see if in fact your model would've worked, let me explain what it means, now suppose. We're looking at some data streams. Perhaps it's, let's stick with that employment. Suppose the unemployment data looks like this for some period of time. Right. And now what you're doing is, is you're saying okay. We've got a model. We're gonna ask how well that model will do. So what you do is you sort of fix that. You give that model data up to here. So it's fitting pretty well. And then at this point. Right here, you say hey, let's see how our model would predict from here on now. If you run your model, it sort of goes like this. If it goes like that, you can say, you know, our model in the past, if we were using the same model in the past, it wouldn't have worked. And so that makes you fairly dubious about whether the model's gonna work now. So, retrodiction, going back and testing past data, is a good way to test how good your model really works. Fifth reason, predicting other stuff. So you might construct a model for one reason. Let's suppose you're really interested in the unemployment rate. You know, you construct a model to predict the unemployment rate. But out of that pops out the inflation rate, so you get something else. This is a good way to tell, you know, how strong your model is.'Cause typically, you construct a model for one reason that gives you other stuff. There's another type of predicting other that's way cool about models. So when they developed the first models of the solar system, right? The heliocentric model, the sun in the center, right? So you've got the sun sitting here in the center, and the planets orbiting. The math didn't quite work out right. And they figured out, there must be a big planet out here. That's causing the orbits of the other planet to be skewed a little bit. And the big planet was Neptune. They couldn't see it. But their model predicted it. So the model predicted something, something else, something other, that was evident in the data. So models can predict stuff. Other than what you expect them to predict. Which was really cool. Alright, six, 63, to inform data collection. So let's suppose that you're interested educational reform which is something I'm interested in. You want to think okay, how do we make better schools? Well, what you can, remember in our last lecture about being a clear better thinker. One thing models force us to do is name the parts. So, I want to think, how are schools, how to make better schools? Well there's a lot of data out there on school performance. So what i want is, is I want some sort of model that explains why students do poorly and why students do well. So you think, well what are the parts of that model? Well it might things like Teacher quality, we call that TQ, right? There might be parental status, we call that PS, whether your parents went to college, whether they got high school degrees, whether they're doctors, lawyers, that sort of thing. There might be total spending in the school district, that might matter, right? Things like class size, just put CS for class size. Class size probably matters a lot. Right? You might argue that, you know, technology. Matters is there technology in the classroom. You might even argue, you know, there's general health. Is health a big consideration. And you can even, you know argue, what is the, what are the other students like in the school? What are the other peer effects? What is the effect of what other students do? So if you don't have a model, you don't even know what data to go get. So models help you to figure, okay, what data should we get, and what data should be included, and what data, what data should we go out there and find, so that use of models can be very useful since it tells you what data to go out there and get. Our last two. For why you model art a little bit different, but they're, they're similar to one another. And that is that we can use data, right? To sort of tell us more about the model, and then we can use the model to tell us more about the world. So let me, let me explain what I mean a little bit. [inaudible] confused. So, one thing that these models force us to estimate hidden parameters in the model. So, here's a, sort of a classic model from. Disease from epidemiology the study of disease, is called the SIR model, so there's three types of people, there's susceptible people, there's infected people, and there's recovered people, so there's a disease you could be susceptible to it, you could be infected, or you could be recovered and when you're recovered then you're immune. You're not gonna get it again. So let's suppose that you know, you work for the Center for Disease Control, and something you see, oh my gosh, people are getting sick. But you don't know, there's some sort of flu going on. But you're not quite sure how this is spreading. Is it spreading, is it airborne, right? Is this virus spreading, you know, through mucus or something? You're not sure. And you're also not sure how virulent it is, so you're not sure how many people are gonna get the disease. What you've got, let's draw a little graph where you get time on this axis. And you've got the number of people. Who have the disease. And, what you can do is you can sort of see. Over time, exactly how many people are getting the disease. Well, if you can see over time how many are getting it from that data, you can predict how virulent the disease is. Like, how likely it is to pass from one person to the other. And that's gonna allow you to figure out, is the disease gonna go like this, or is it gonna go like that? And so, from that data, you can estimate hidden parameters, right? Namely, how virulent the disease is. Like, you can't tell by looking at data how likely one person is to get it from another. You know, from just, you can't tell by looking at the world. But by looking at how many people get it, you can go back and estimate. That parameter. You can figure it out. That's what's really cool. Alright? Last reason, calibration, so calibration refers to sort of constructing a model and then calibrating it as close as possible to the real world. Let me give an example here. So suppose I want to write a model of forest fires. So I'm going to draw some really bad trees here. Here's a tree. Here's another tree, right. And I want to know what's the probability, these are horrible trees, what's the probability that the fire moves, right, from this tree to this tree. How fast does it move and all that sort of stuff. Well what I can do, what I can gather is if the state exists, tons of data about past forest fires, and with that past data I can calibrate a really accurate model of forest fires. How likely are they to spread? How you know their speed depends on how dry the trees are, how much precipitation there's been, what the wind speed is, all that sort of stuff. Once I've got all that data that would allow me then to figure out. You know, how dangerous are particular forests? Right? I could say, oh my gosh, northern New Mexico hasn't had rain in over two years. Here's how dry the soil is. Here's how dry the trees are here is, you know, how many acres of forest we have, here's what the wind speed is, and you can know exactly how dangerous a particular forest happens to be at that particular moment in time. So you use all sorts of past indexes to calibrate a particular model, you know, your big model and then you can use that model. To construct policy. And that's what we're going to talk about in the next lecture, right, how do we use models to make decisions, to strategize, right, and to design things. Thank you.