So say we're all pros in making Bayesian networks.

You just sat down and made this wonderfully,

very sparsely connected 20 node network.

Now what do we do?

Of course, now we come to the inference.

Actually in practice, we've written down onto a blackboard

this wonderful Bayesian network.

What we do is actually we pull down from

the Internet a Bayesian network package,

then we type it in,

in their input syntax,

which is relatively simple,

which is essentially a bunch of CPTs.

Then we make a little query,

what's the probability of coming down with

a fever given that you have a runny nose and so on.

You press the button and it says 0.32.

Okay, not 3.2 I hope.

Okay. That's what you do in practice.

Of course, in class,

we have to go the hard way

and understand what's going on.

So, typical thing.

So, we're observing evidence variables

and trying to draw conclusions on query variables.

Essentially, what's the probability distribution of

burglary given that John indeed called?

What's the probability of

burglary given that John calls and Mary calls?

Those kinds of things.

So, that's the typical thing we

call a probabilistic inference tasks.

So, you have a set of query variables.

We have a set of evidence variables.

I think those should actually not be the same.

We have an event that assigns values to E and we wish to

compute the probability distribution

of the query variables given the evidence.

I'm sorry, I'll have to try to remember to fix those errors.

Okay. Of course, we assume that we have a Bayesian network.

We're going to right now just basically

make the query variables a singleton.

Nothing hinges on this,

but it just makes writing down things much easier.

So, if we have this example,

we have a burglary,

what's the distribution of the values of burglary given that John calls and Mary calls?

Then X is burglary,

nice singleton, and then E is those two values,

and why, of course,