So in a way, Bayesian networks are just a compilation of this method into something that's much easier to do in practice.

Okay, so let's go back to our example, cavities and catch.

This is what we did, normalization, marginalization, we used the chain rule, we exploited conditional independence.

And the important thing was that when we want to compute this term about XI in the chain rule somewhere in here,

then I only need to look at the parents of something, which is usually a very small subset given some graph like that.

What can you do by these things? Medical diagnosis, we already saw that.

This is a system that actually gives you the Bayesian network, and the nodes are all random variables.

Does the patient have pneumonia? And you want to look at, say, the temperature, right?

That's not actually a finite domain. Well, with humans, probably it is a finite domain, random variable.

And so on. And those are connected, and the thing you should realize here is that this is not a fully connected graph.

That's the default. Everything can have an effect on everything else. Well, the world isn't like that.

Even though temperature and pneumonia, they are connected, many of the other things aren't.

And that gives us conditional independence, and so on.

You use these kind of things in face recognitions, very important self-localization of robots,

where you need to know something about influences of certain geographical features on each other.

Remember, we had this example of seeing the Eiffel Tower or not, and what's involved with that.

And there's things where you basically do things like nuclear test bands or so.

Many, many systems actually involve what is often called graphical novel, not novels, but models.

So a model you can inspect graphically.

So what are we going to do? We're going to define them, Bayesian networks.

What is the meaning of those funny objects? How to construct them? And how to do inference?

Those are the next things we're going to look at.

And of course, inference on Bayesian networks is our primary concern. Inference like we did for the Wumpl's world.

And of course, it's going to be important to understand what the complexities are.

How does the design of our graphical model influence the inference capability of our system?