Difference between revisions of "ECE662 hw2 discussions" - Rhea

Revision as of 15:28, 9 April 2010

MATLAB has a "mle" function for maximum likelihood estimation. I think that this function is useful to verify the result of hw2 if you have MATLAB. I try to find the effect of the sample size in MLE using "mle" function because the number of samples is critical for estimation. To do this, I generate samples from normal distribution with mean as 0 and std as 5. The below graph shows the results of MLE according to the number of samples.

The code for this graph is like below.

   samples_step = 3;
   num_samples = samples_step:samples_step:10000;
   len = length(num_samples);
   mu = 0;
   sigma = 5;
   muhat = zeros(1, len);
   sigmahat = zeros(1, len);
   for x = num_samples
       data = mu + sigma * randn(1, x);
       phat = mle(data(1, :));
       muhat(1, x/samples_step) = phat(1);
       sigmahat(1, x/samples_step) = phat(2);
   end
   plot(num_samples, muhat);
   hold on;
   plot(num_samples, sigmahat);

--Han84 22:49, 2 April 2010 (UTC)

Need real database? Look it up in this website:

http://archive.ics.uci.edu/ml/datasets.html

have fun!

Golsa

Cholesky Decomposition

I wrote this MATLAB / FreeMat code to compute the Cholesky Decomposition of a matrix. The matrix A should be real and positive definite.

   function L = cholesky(A)
       N = length(A);
       L = zeros(N);
       for i=1:N
           for j=1:i-1
               L(i,j) = 1/L(j,j) * (A(i,j) - L(i,1:j-1)*L(j,1:j-1)');
           end
           L(i,i) = sqrt(A(i,i) - L(i,1:i-1)*L(i,1:i-1)');
       end
   end

You can use the resulting lower triangular matrix L to generate multivariate normal samples with covariance given by the matrix A by computing

X = $ \mu $ + L Z, where Z is iid standard normal.

Pritchey 20:28, 9 April 2010 (UTC)