CS2710 / ISSP 2160: Homework 4

Uncertainty and Probabilistic Reasoning (Chapters 13-14)

Assigned: November 6, 2006

Due: November 20, 2006 (by beginning of class, via both dropbox (at least for non-graphical parts) and hardcopy). Please write your Pitt email alias on your hardcopies.

Programming Assignment (40 pts)

1. Bayesian Inference

For this homework you will utilize a Java implementation of Bayesian inference (JavaBayes) to apply some of the concepts we learned in class to the Wumpus world.

In particular, you will use the JavaBayes system to implement a Bayesian network for computing the probability of a wumpus in a location given stench information.

  • Download and install JavaBayes from www-2.cs.cmu.edu/~javabayes. Follow the instructions to run JavaBayes.
  • Use JavaBayes to create the Bayes network shown below. You may assume a 10x10 wumpus world with one stationary wumpus, where each cell is equally likely to contain the wumpus. Save your network to a file.
  • Use the network to compute the probability of a wumpus with no stench information, then one stench, then two stenches, then three stenches, and then four stenches. This can be done by using the "Observe" feature to set a stench node to true, and then use the "Query" feature to query the probability of the wumpus node. This information will be printed to the console window, which you should then save to a file.
  • Collect the wumpus network file with no evidence, a file with an explanation of your rationale for the CPT values of each node, and the file containing the dump of the console window.

    Paper Problems (60 pts)

    2. Probability (10 pts)

    Of the entire population, 2% has a certain disease X. A test Y, which indicates whether or not a person has the disease, is not 100% accurate. If a person has the disease, there is a 6% chance that it will go undetected by the test. However, there is also a 9% chance of "false alarm" (meaning that the person does not have the disease but the test indicates otherwise). A person Z takes a test which later comes out positive (meaning that the test says he has the disease). What is the probability of this person having the disease in reality?

    3. Probability (10 pts)

    13.6 (Russell and Norvig, p. 489)

    4. Bayesian Networks (10 pts)

    Consider the Bayesian network with the following topology: A is a parent of B and C, and B and C are parents of D. Furthermore, A, B, C, and D each could have a value of either true or false. Finally, the CPTs for each node are as follows:

    P(A) = 0.75

    P(B | A) = 0.2
    P(B | not A) = 0.5

    P(C | A) = 0.7
    P(C | not A) = 0.25

    P(D | B and C) = 0.3
    P(D | B and (not C)) = 0.25
    P(D | (not B) and C) = 0.1
    P(D | (not B) and (not C)) = 0.35

    If we know that A is true, what is the probability of D being true?

    5. Bayesian Networks (10 pts)

    14.1 a-d (Russell and Norvig, p. 533)

    6. Bayesian Networks (10pts)

    14.2 a, c, d (Russell and Norvig, p. 533-534)

    7. Bayesian Networks (10 pts)

    14.3 a-b (Russell and Norvig, p. 534)