Simon Fraser University

Spring 2004

CMPT 882

Instructor: Oliver Schulte

Due: Tuesday, March 9, in class.

Topic: Evaluating Statistical Hypotheses.

Paper and Pencil:

1. Exercise 5.2, 5.3, 5.4 from Mitchell.

2. Consider the EM algorithm for finding a maximum likelihood model for the mixture of two Gaussians, as described by Mitchell in Section 6.12.1.

Assume the following settings:

      The initial hypothesis h for the mean of the first Gaussian, mu1, is 0

      The initial hypothesis h for the mean of the second Gaussian, mu2, is 1

      The variance sigma^2 is 1 for both distributions.

      The observed value xi is 0.

Carry out one step of the EM algorithm with these initial settings (i.e., find a new hypothesis h’ = <mu1’, mu2’>). Discuss briefly whether intuitively the estimate h’ seems to be more likely given the observed value than the initial hypothesis.