Bayesian Nets Homework

Updated 10/17/2005

HOMEWORK MOTIVATION: By the time you face this tutorial, we will have talked about the mathematics of probability a lot in class and done some work with Bayesian reasoning.  Bayesian reasoning becomes more powerful when we find a way to translate our understanding of cause and effect into graphical representations that use Bayesian reasoning and conditional independence.  

GOAL: Understand the semantics of Bayesian networks and how to do some simple inference using these networks.
  1. Consider the Bayesian network and conditional probability tables shown in Figure 14.2 on page 494.  Compute the following:
    1. The probability that John calls, Mary does not call, the Alarm goes off, that a burglary is occuring, and that no earthquake is occuring.
    2. The probability that John and Mary both call given that a burglary is going on and that no earthquake is happening.
    3. The probability that an alarm is not on given that an earthquake is happening and no burglary is happening.
  2. Draw the Bayesian network associated with the following joint distribution function: P(A,B,C,D)=P(A)P(B|A)P(C|B)P(D|B).
  3. Draw the Bayesian network associated with the following joint distribution function: P(A,B,C,D)=P(A)P(B)P(C|A,B)P(D|C).
  4. Consider the Bayesian network shown in Figure 14.18 on page 533.  Do the following:
    1. Write the formula for P(Radio,Battery,Ignition,Gas,Starts,Moves) in terms of the conditional probability relationships illustrated in the figure.
    2. Make up legal values for all necessary conditional probability tables.  Specify the values that the variables can take on.