problem set6

problem set6 - ELEC 531: STATISTICAL SIGNAL PROCESSING...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
ELEC 531: STATISTICAL SIGNAL PROCESSING Department of Electrical and Computer Engineering Rice University Fall 2007 Problem Set 6 Due: October 25, 2007 Problem 6.1 The EM algorithm and mixture densities. Suppose we observe L iid realizations X = ( X 0 ,...,X L - 1 ) from the mixture density pf ( x )+(1 - p ) g ( x ), where p is unknown. We would like to find the maximum likelihood estimate of the nonrandom parameter p . The EM solution is to augment the observed (incomplete) data X with Z = ( Z 0 ,...,Z L - 1 ), where Z l tells which component of the mixture X l came from, i.e. X l | z l =1 f ( x l ) and X l | z l =0 g ( x l ) , and Pr( Z l = 1) = p . (a) Show that the EM iterations are given by ˆ p ( k +1) = 1 L L - 1 X l =0 ˆ p ( k ) f ( x l ) ˆ p ( k ) f ( x l ) + (1 - ˆ p ( k ) ) g ( x l ) . (b) Create a MATLAB script that uses the EM algorithm to compute the maximum likelihood estimate of p for the two cases where the true value of p is 0 . 5 and 0 . 8. Assume that
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This homework help was uploaded on 02/11/2008 for the course ELEC 531 taught by Professor Lexa during the Fall '07 term at Rice.

Page1 / 2

problem set6 - ELEC 531: STATISTICAL SIGNAL PROCESSING...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online