Open course ware

In this segment we provide a high level introduction into the conceptual framework of classical statistics. In order to get there, it is better to start from what we already know and then make a comparison. We already know how to make inferences by just using the Bayes rule. In this setting, we have an unknown quantity, theta, which we model as a random variable. And so in particular, it's going to have a probability distribution. And then we make some observations. And those observations are modeled as random variables. And typically we are given the conditional distribution of the observations given the unknown variable. So these two distributions are the starting points, and then we do some calculations. And we use the Bayes rule. And we find the posterior distribution of theta given the observations. And this tells us all that there is to know about the unknown quantity, theta, given the observations that we have made. What is important in this framework is that t...

PROFESSOR: Random walks provide probabilistic models for a bunch of settings. In fact, we've seen a couple already, so let's examine what they are in general. So the set up for a random walk is that you have a digraph, and we can also often think and talk about the digraph as though it was a state diagram for a machine with state, so here's a three-state digraph-- blue, orange, and green-- and the part that becomes probabilistic is that we think of the process of which edge to follow when you're at a given state is made probabilistically. And the only rules are that we're going to assign probabilities to the edges in a way like this where, for example, what I'm telling you is there's a 1/3 probability that I'll follow the edge from O to O, and a 2/3 probability that I'll follow the edge from O to green, and the rule is simply that the sum of the probabilities on the outgoing edges has to sum to 1. So let's fill in the rest of the gr...