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)
Hidden Markov Models
Question, can I implement hidden markov models and then Baulm-Welch algorithm for this homework? Because this is also a kind of parametric density estimation and is also maximizing the likelihood. In this case, some of the suggestions on the homework page won't be very well corresponded, will this matter? Thanks!
--Yuanl 19:10, 10 April 2010 (UTC)
