Good.

There's only one way to really understand this,

is make your own networks.

And make your own inference here.

So we do probabilistic inference,

which we have defined.

And I was kind of confused yesterday

about these numbers x and these numbers n,

but it's actually not the size of these net literature subsets.

So it's perfectly fine here.

So we always want to find out what's

the probability distribution of a single variable,

given some evidence.

And we always do, as you know why, this computation,

which we will now look in a little bit more detail.

Can we actually make this computation

we've been having at the board for a couple of times,

can we make that more efficient?

So we end up essentially with, in this thing here,

we end up with essentially this formula,

with the real problem here that we're interested in.

We now can order these things.

We use conditional independence.

And we can see we have a double sum here

over this five factor multiplication.

And then we can do the usual tricks.

We can move variables outwards across sums

that don't affect them.

And if you do that, and we do this,

then you get up in this example with a formula

that looks like this.

Now you can actually see it.

And now you can start analyzing.

We have a factor here, p of b.

I'm just realizing this is only half of the formula,

because we have a p of not b factor which I've eliminated,

because it looks exactly like this.

But do we?

Yes, no, no, no.

Yes, we have a second factor, but it wouldn't fit.

So if we move out everything, what we're seeing

is we're seeing a tree-shaped formula, where we're first

looking at the value of b.

Then we're doing a case distinction on whether e or not

e is the case.

And then we're making a case distinction on a or not a.

When you see formula as a computer scientist,

of course, the first thing you think is, ah, tree.

Here's kind of the decision tree that I've kind of

tried to show you here.