We live in a complex world with diverse people, firms, and governments whose behaviors aggregate to produce novel, unexpected phenomena. We see political uprisings, market crashes, and a never ending array of social trends. How do we make sense of it? Models. Evidence shows that people who think with models consistently outperform those who don't. And, moreover people who think with lots of models outperform people who use only one. Why do models make us better thinkers? Models help us to better organize information - to make sense of that fire hose or hairball of data (choose your metaphor) available on the Internet. Models improve our abilities to make accurate forecasts. They help us make better decisions and adopt more effective strategies. They even can improve our ability to design institutions and procedures. In this class, I present a starter kit of models: I start with models of tipping points. I move on to cover models explain the wisdom of crowds, models that show why some countries are rich and some are poor, and models that help unpack the strategic decisions of firm and politicians. The models covered in this class provide a foundation for future social science classes, whether they be in economics, political science, business, or sociology. Mastering this material will give you a huge leg up in advanced courses. They also help you in life. Here's how the course will work. For each model, I present a short, easily digestible overview lecture. Then, I'll dig deeper. I'll go into the technical details of the model. Those technical lectures won't require calculus but be prepared for some algebra. For all the lectures, I'll offer some questions and we'll have quizzes and even a final exam. If you decide to do the deep dive, and take all the quizzes and the exam, you'll receive a Course Certificate. If you just decide to follow along for the introductory lectures to gain some exposure that's fine too. It's all free. And it's all here to help make you a better thinker!
Linear Models
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来自 University of Michigan 的课程
模型思维
1113 个评分
从本节课中
Learning Models: Replicator Dynamics & Prediction and the Many Model Thinker
In this section, we cover replicator dynamics and Fisher's fundamental theorem. Replicator dynamics have been used to explain learning as well as evolution. Fisher's theorem demonstrates how the rate of adaptation increases with the amount of variation. We conclude by describing how to make sense of both Fisher's theorem and our results on six sigma and variation reduction. The readings for this section are very short. The second reading on Fisher's theorem is rather technical. Both are excerpts from Diversity and Complexity.
与讲师见面
Scott E. PageProfessor of Complex Systems, Political Science, and Economics
Center for the Study of Complex Systems
Hi. In this lecture we're gonna talk about prediction, And what we're gonna do is
we're gonna go back and look at some of the models we learned earlier in the
class. Particularly we're gonna look at the category models we looked at, and the
linear models we looked at. And we're gonna show how those were, in fact,
predictive models, And how they enabled us to get estimates of what, something that
was gonna happen in the real world. So first let's just talk about a basic
predictive task. Like, suppose I said to you, predict the height of the Saturn five
rocket. Now, what you typically do is you might think, well, the Saturn five rocket
is like blank, something else. And if you thought of the Saturn five rocket, Like
let's say a water tower, You might guess that it's 100 feet high. Or alternatively
you might say the Saturn type rocket is like the Statue of Liberty. And then you
might guess that it's about 400 feet high. Or you might even think that the Saturn
type rocket is like the empire state building and you might guess it's a 1,000
feet high. So different people used to run categories and, therefore, make different
predictions. Now this idea that people put things in different categories we talked
about before in terms of the phrase lump to live to use these categories to make
sense of the world. And to make sense of the world, what we're really doing is
predicting. Now let's go back to the example used in class about different.
Food items like apples, pears, cakes, pies, those sort of things. And they all
have different calories. Well, if we just sort of think how much calories the food
have, there's a lot of variation in there. And we can compute the variation in total
calories here. Remember, we got this massive number. The total variation was
53,000. But when we think about things like, bananas we think about them
differently than cake, we put them in different categories. And these categories
enable us to make better predictions. So, for example, we've created a fruit
category and we've created a dessert category. And when we did that, we could
then make predictions about how many calories fruits have and how many calories
desserts have and then reduce the variation. So, for example, a fruit had a
mean of 100, and our desserts had a mean of 300 and the variations were only 200
and 5,000. And so what we got was, initial variation was 53,000, but afterwards we
only had 5,200 variation left over, so we explained a lot of the variation, and we
described that in terms of r squared, which was the percent of variation
explained, and in this case that was 90%. So let me talk about, this is just a
review of what we did. Let me talk about what this means. You create categories.
These categories produce variation. The less variation you have, the better you
are at predicting If different people use different categorizations. Then they're
going to make different predictions and that's what we want to think about in this
set of lectures. We want to think about how people create these categories and
make predictions and think about accurate individual categories, categorization.
Then we want to think about accurate collective categorizations, that's the
idea. But categories aren't the only way we thought about improving predictions,
remember we also talk about people using linear models, let's see how people can
use a linear model to predict. So remember a linear model we get sort of say, Z
equals AX plus BY plus CZ plus a constant. And this Z is called the dependent
variable and X, Y and Z are called independent variables. And that gives X, Y
and Z very, and they determine the value of Z. So let's suppose I ask you to figure
out how many calories there are in a sub. Well you could write a linear model of the
calories in a sub. You'd say the calories in a sub depends on the bun, the mayo, the
ham, the cheese, the onion and the tomato. All those sorts of things and you just
decompose the total calories into all the things that's comprised that sub. And this
is a very different approach than categorization. Categorization would say,
well a sub is sorta like cake. And cake is 400 calories. Or a sub's like a banana and
a banana has 100 calories. This is the different approach. It's a different
model. So what we're gonna see is that different models can end up being useful.
But let's, let's think about this just for a second. You're gonna make this
assumption that the calories from the sub, because the sum of the parts. And
sub-calories are linear, there are no interactions in terms of calories. So if
we do this, we're gonna get that the bun has possibly 300 calories, the mayo has
200, and the ham has 50, and so on, and we get a total of 665. Now it's interesting
that I had my students do this in a class I was teaching and we got this number 665.
And then we looked up how many calories were in a sub from the local sub shop and
the answer was 683. So our model was really, really accurate, which is cool. So
that's the idea I want in the back of your mind as we move forward. The idea that.
You could reason by categories, people could have different categories. You can
reason by linear models and people can have different linear models. But we make
these predictions and these predictions have some level of accuracy. In the case
of categorical models we think about accuracy in terms of R squared, the
percentage of the variation explained. In the case of linear models we do the same
thing, we think in terms of the percentage of variation explained. When we try and
understand the wisdom of crowds, which is where we're going to go next, we're going
to ask sort of how much variation is in the crowd's prediction, how far off is the
crowd. Okay. But a crowd you wanna think consists of people. And those people have
models. And those models can differ and the reason they can differ is cause people
use different categorizations to these different models. Some people use linear
models. Some people might use markup models. Some people might use percolation
models. And it's that model diversity that's gonna end up being so useful. All
right, Thank you.
