Bayesian Network based on outcomes

Question

I'm pretty new here, but have a question that I would like some help with. I'm studying machine learning and specifically Bayesian Networks. The problem I am trying to solve is:

Consider a cow that might have a disease. You can detect this disease with a milk test that has a false positive rate of .05 and a false negative rate of .01. This test is done for 5 days in a row, with 5 outcomes. Given a set of outcomes, determine the state of the disease. Assume that the prior probability of an infection on day one is 0.001, and that the state of infection at a given day depends only on its state at the previous day, such that the probability that an infection would persist to the next day is .70, while the probability of a new infection is 0.002.

Your then given a set of outcomes and asked to determine some stuff based on those outcomes. I'm not quite sure how to construct the network for this problem and was wondering if anyone had some pointers.

Thanks.

Answer 1

The Bayesian network should have the following structure:

• infectn says whether the cow is infected on day n
• testn gives the result of the test on day n

Answer 2

As shown in the diagram, this is a so-called "hidden Markov model" (HMM). Searching for that term should turn up a lot of info.