ELEC
problem set6

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

• Homework Help
• PresidentHackerCaribou10582
• 2

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

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 f and g are unit variance Gaussian densities with means 0 and 1, respectively.

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

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern