EECS 391/491 PS#8 FAQ

EECS 391/491: PROBLEM SET #8 FAQ

You can do Problem 8.1 with the information from Lecture #16. You can do Problem 8.3 given Lecture #17 and the example below. You should be able to do Problems 8.2 and 8.4 entirely (or make a good start) as well before seeing Lecture #18.

An example of Bayes' net reasoning to get you started

Consider the robot example from lecture:

B = battery is charged
M = arm moves
L = object is liftable
G = gauge reads that battery is charged

What is P(~g, ~b, ~m, l) ?

  P(~g, ~b, ~m, l) = P(~g|~b) P(~m|~b,l) P(~b) P(l)           (Eq. 1)
                   = (0.9) (1) (0.05) (0.7)                   (Eq. 2)
                   = 0.63/20 = 0.0315
                     
(Eq. 1) comes from the chain rule and the conditional dependencies
in the graph of the Bayes network: 

  P(node|nondescendents(node), parents(node)) = P(node|parents(node))

(Eq. 2) is filled in from the Conditional Probability Tables (CPTs)

Problem 8.2

See Section 14.4

Problem 8.4

Converting from odds to probabilities. The probability that a '3' will not be thrown on a die is 1 minus 1/6 = 5/6. This gives odds of 5 to 1 against throwing a '3'.

When asked to calculate "the probability that the battery is low given the observer's report," this requires computing both

P( battery is low | observer says that Orville drops )
P( battery is low | observer doesn't report thta Orville drops )

Problem 8.5

We will cover fuzzy sets in Lecture #18. To specify the fuzzy sets, draw membership functions, such as in the last page of the Lecture#18 eHandout.

Problem 8.6

In particular, use rejection sampling (page 513 of R&N).

Note: you do not have to implement the general algorithm, just solve the specific problem at hand.

An example Monte Carlo program (using rejection sampling) is provided in the Lecture#18 eHandout.

Technically, you don't have to perform rejection sampling here because there is no evidence (i.e., every sample is consistent with the evidence). So, you really only have to do "direct sampling" for the particular atomic event given.

Problems 8.7

You may wish to consider likelihood weighting (R&N, pp. 514-515). Note: as before, you do not have to implement the general algorithm, just solve the problem at hand.

Author: Michael S. Branicky.