To change this example even further.

How did we get this?

Here are my answers.

We now apply Bayes rule.

Suppose we multiply two Gaussians as in Bayes rule a prior and a measurement probability.

The Bayes network is composed of 2 variables, A and B.

And here's my code, this implements Bayes rule.

And see what happens. It multiplies.

So this is the essence of Bayes Rule, which I'll give to you to you in a second.

In the M step we now figure out where these parameters should have been.

We apply the same trick as before where we use the exact same prior of 0.01.

And what we care about is what's our prior probability of spam that maximizes the likelihood of this data?

Here is our sequence. There's a couple of sunny days 5 in total a rainy day, 3 sunny days, 2 rainy days.

This makes Bayes Rule really simple.

This expression is called the likelihood.

So, the probability of given that we don't have cancer is 0.2, but the prior here is 0.99.

This gives us 0.0009.

We normalize this by the same expression plus the probability for the non spam case.

And just like before, we multiply the prior, this guy over here, that gives you 0.3.

You remember that we cared about a grid cell xi, and we asked what is the chance of being in xi after robot motion?

This was exactly the same as in our diagram in the beginning.

So therefore the answer to this question would be 0.5, or half.

Why is this?

You remember this because that's what you programmed.

For example, for the prior probability, we found that 3 8 messages are spam.

If I now change some parameters say the robot knows the probability that it's red, and therefore, the probability 1 is under the green cell as a prior.

So suppose we know we are looking at faces.

In maximum likelihood estimation, we assign towards our probability the quotient of the count of this specific event over all events in our data set.

Now, you're not smart enough to tell anybody anything,

Colorcoding saves time.

Our likelihood is the probability of seeing a positive test result given that you have cancer multiplied by the prior probability of having cancer over the probability of the positive test result, and that is according to the tables we looked at before 0.9 times a prior of 0.01 over now we're going to expand this right over here according to total probability which gives us 0.9 times 0.01.

So I want you to program this in the IDE where there are three input parameters P⁰, P¹ and P².

To make this correct, we also have to compute the posterior for the non cancer option, which there is no cancer given a positive test.

So for example, we observed that we always have a single first day, and this becomes our prior probability.

Thrun So we just learned a number of things.

In this example, we again might have our unobservable cancer C, but now we're running 2 tests, test 1 and test 2.

But let me just derive it formally. The transition probability of going from A0 to A1 is 0.5, times our prior probability, which is one ninth, and we get the same 0.5 over here, times the prior probability of eight ninth.

Use Laplacian smoothing with k 1 to compute the probability of a movie being old this is a prior probability, which is just based on class counts the probability of the word top as a title word in the class of old movies, and the probability that a new movie that we look at by new I mean a movie we've never seen before that is called top, the probability this movie that corresponds to the old movie class with the new movie class.

This form is easily transformed into this expression over here, the probability of the message given spam times the prior probability of spam over the normalizer over here.

This white line is year over year inflation growth, and let me do that in white.

You led them into combat.

What is your probability of winning and before we can think about that, think about how you would win if you always switched.

Saying what you think frankly is not a bad thing.

It comes down to here. But notice once again, although here it's pretty close, but utilization dropped off a couple of quarters before inflation dropped off.

The sum or set of all those vectors together form the belief space.