Hi, my name is Brian Caffo and welcome to this Statistical Inference Coursera Data Science class. In this class, we are gonna learn about the process of formal statistical inference. So I define statistical inference as the process of generating conclusions about a population from a noisy sample. Without statistical influence, we're simply living within our data. With statistical inference, we're trying to generate new knowledge. We're trying to extend beyond our data to a population to give answers. With statistical inference, our estimators have actual things that they're estimating. And in fact, I would say statistical inference is the only formal system of inference that we have. Let me give you some examples. Hopefully you'll understand what I'm talking about. Consider trying to predict who's going to win an election on election day, given a sample of likely voters today. Well, there our sample is a noisy dataset. Some people might not actually vote on election day. Some people might change their mind as to what they're going to say now. Or some people be deliberately misleading. So we'd like to try to draw together all that uncertainty and use that to predict who's gonna win on election day. When a weather man tells you the probability that it rains tomorrow is 70%, they're trying to use the historical data that is particularly the most recent data, to predict tomorrow's weather and actually attach a probability to it. That probability refers to a population. An example that's very close to the research I do is trying to predict what areas of the brain activate when we put them in an fMRI scanner. In that case, people are doing a task while they're in the scanner, for example, tapping their finger or something like that. And we like'd to compare when they're tapping their finger, to when they're not. And try to figure out what areas of the brain are associated with finger tapping. That's just one example there. Again, these are all very different aspects of statistical inference. They're very different in the ways in which we're thinking about and modeling the randomness. And so I think you'll probably get the sense that statistical inference is a kind of challenging subject because of that. One thing I want to mention briefly and hopefully get out of the way as early as possible is the idea that there's many different modes of statistical inference. And, in fact, there's a recent New York Times article that described the difference between so-called Bayesians and frequentists, two different kinds of inferential paradigms. And I think when you first come into this discipline, you might even be surprised that there can even be more than one way to think about statistics. But, in fact, even amongst so called Bayesians and even amongst so-called frequentists, there's all different variations and shades of grays, and there's many a Bayesians that I would say just really behaved like frequentists and so on. So, what we're gonna do in this class to make it as straightforward as possible is to pick a very particular paradigm, this frequentist paradigm, that's the one that's most commonly taught in introductory statistics classics. The reason I elected to do this is because it's the most likely one that you'll encounter in practice. And also, I think once you've develop some of these fundamentals, you'll be able to extend this knowledge to lots of different areas and you'll be able to build on it. So we wanna build a good foundation. We're going to do it with sort of frequency style thinking. What I mean by frequency style thinking is, we're gonna think of probability like how we think of gambling. So I'm gonna think the probability that a coin winds up as heads is gonna be, if I were to flip it maybe infinitely many times, and there's all this randomness that I'm thinking about in the coin flip, and the proportion of heads would really define a sort of intrinsic probability of the head to the coin. That's a frequentist style of thinking. It's sort of the idea that we can repeat an experiment over and over and over again and the percentage of times that something happens defines that population parameter. There is more than one way to think about probability, and more than one way to think about inference. But we're gonna focus on specifically frequency styling inference like that. Like the coin flipping and all the gambling experiments that we're very familiar with and we're gonna leave all that other stuff to the side. In the notes, I give you some examples of all different sorts of topics that you can try to build on after you've mastered some of the tools from this class. Let me give you just a quick example. There's a thriving community now that's trying to figure out how can we really infer causation, not just association, but real causation using noisy statistical data, and that's a very deep problem. And what they'd like to do is enumerate the assumptions and a set of tools and statistical study designs that will lead us to develop causality rather than association. That requires us to do things like define what we mean by something causing something else. It's a very deep field and at any rate, that's one example of the couple I give in the notes where you can build on this. For example, survey sampling, epidemiological studies and so on. But again, what I'd like to do in a very short class like this is really focus on building our foundation in basic frequency style probability models and testing. So I'd like to welcome you to the class. The way that you want to think about this class is, if you're sort of keeping pace with it, it's a four-week class. But if you're struggling with some of the concepts, don't feel badly about having to extend this class out, take it twice. This is deep stuff and it's unusual I think, and it's not the math and it's not the, I know many mathematicians who really struggle when they first start thinking about statistical inference cuz it's just a different way of thinking about the world. So think of this as a four-week class. And if you're getting it, if you're not, take a little bit more time. There's four quizzes. There's one project. The project, I really think drives home some of the central ideas of inference. So I hope that you would spend a fair amount of time thinking about the project because it really drives home what we mean by sampling distributions and what is meant by frequency style statistical inference. The quizzes will be auto-graded. They're, ideally, due at the end of each week but you can attempt all the quizzes from the start of the class. I've put out some homework problems and I've linked those homework problems to the specific quiz questions so you can practice before you even try the quiz. So welcome to the class. I'm really enthusiastic about teaching you. I really like inference. It's my favorite subject. I've been studying statistical inference for probably 15 years now. And every time I think about it, I learn something new. And so I hope you can really dive into this deep and incredibly important subject with me.
