8 – 35 – Two Test Cancer 2 Solution V4

We have tried the same trick as before, where we use exact same prior of first plus gives the following factors, 0.9, 0.2. But our minus gives us the probability 0.1 for a negative test result treatment of cancer. And a 0.8 for the inverse of a negative result of not getting cancer. You multiply … Read more

6 – 33 – Two Test Cancer Solution V4

So the correct answer is 0.1698 approximately. And to compute this, I used the trick I’ve shown you before. Let me write down the running count for cancer, and for not cancer, as I integrate the various multiplications in Bayes rule. My prior for cancer was 0.01, and for non-cancer was 0.99. Then I get … Read more

4 – 31 – Computing Bayes Rules Merged FINAL

So we just encountered our very first Bayes network and did a number of interesting calculations. Let’s now talk about Bayes Rule and look into more complex Bayes networks. I want to look at Bayes Rule again and make an observation that is being non-trivial. Here is Bayes Rule, and in practice what we find … Read more

35 – 62 – D Separation 3

This leads me to the general study of Conditional independence in Bayes Networks that works often called D-Separation or Reachability. D-Separation is best studied by so called Active Triplet’s and Inactive Triplet’s. We have Active Triplet’s render variables dependent and Inactive Triplet’s render them independent. Any chain of three variables like this makes the initial … Read more

33 – 60 – D Separation 2

In this specific example, the rule applies very, very simple. Any two variables are independent, if they’re not linked by just unknown variables. So for example, if we know B, and everything downstream of B, becomes independent of anything upstream of B. E is now independent of C, conditioned B, however, knowledge of B does … Read more

24 – 51 – General Bayes Net

So we are now ready to define Bayes networks in a more general way. Bayes networks define probability distributions over graphs of random variables. Here’s an example of a graph of five variables and this Bayes network defines the distribution over those five random variables. Instead of enumerating all possibilities of combinations of these five … Read more