You accumulate knowledge throughout your life in memories.

I think we're ready to substitute into the Bayes' formula, which we Bayes' Theorem that we rederived.

Put differently, p(Z) is the sum over all i of just this product over here.

And the answer is surprisingly high. It's 25 26, or 0.9615.

You wrote an algorithm that implements what's called Markov localization.

My resulting probability will be 1 α of the non normalized probability.

It might still see a door here, but it's just less likely.

P of R given H and not S can be inverted by Bayes' rule to be as follows.

So let's see if we can solve the probability that we picked a fair coin, given that we got four out of six heads.

Now I'm going to make it a little bit more formal.

Let's now talk about Bayes Rule and look into more complex Bayes networks.

Thrun

So Bayes' Theorem and let me do it in this corner up here.

And we're going to apply the exact same mechanics as we did before.

This has nothing to do with total probability and all with Bayes Rules, because I'm talking about observations.

It was invented by Reverend Thomas Bayes, who was a British mathematician and a Presbyterian minister in the 18th century.

What's the probability of rain on day 1 given that I observed that I was happy on day 1?

So that's the definition of what it means to have the best correction.

Here we had one probability to estimate.

Now both these sources of information carry important information.

So this should be an easier question for you to answer.

Now, this line together gives me the correct probability for the variable i and j.

And the answer is 0.1667 or 3 18.

And then this whole area is the probability that you get four out of six heads.

And the reason why the probability went down is if you look at happiness, happiness is much more likely to occur on a sunny day than it is to occur on a rainy day.

Thrun

So, we've just learned about what's probably the most important piece of math for this class in statistics called Bayes Rule.

Armed with this number, the rest now becomes easy, which is we can use Bayes' rule to turn this around.

Let's look into measurements, and they will lead to something called Bayes Rule.

Theorem, and I think that'll give us a good framework for the rest of this problem.

So what have you learned?

And then we played around a little bit and we got this.

Why is this?

So, suppose for a moment we also care about the complementary event of not A given B, for which Bayes Rule unfolds as follows.

And let me give you a bit of an intuition, visually, kind of with Set Theory, on why that makes sense.

He says, Yes, it burns, but you know that the probability of this being a lie is 0.1.

So, the probability of either of these sequences of flips is 12.5 if the coin is fair and only 8.1 if the coin is loaded.

I will look at Bayes Rule again and make an observation that is really non trivial.

So that's a visual representation of

So dividing 0.0008, the non normalized probability, by 0.1007 gives us 0.0079.

We know this simply because the probability of having a loaded coin at all is zero.

Then I get my first , and the probability of a given they have cancer is 0.9, and the same for non cancer is 0.2.

First to make my life easier, I'll just store the current value of the probability of heads.

We will observe that P of A given X1, X2 and not X3, the expression on the left can be resolved by Bayes' rule into this expression over here.

Given the probability that a test will come out positive.