drbenvincent

%% true probability distribution
true_func = @(x) betapdf(x,1+1,1+10);

%% Do importance sampling
N = 10^6;
% uniform proposal distribution
x_samples = rand(N,1);
proposal = 1/N;
% evaluate for each sample
target = true_func(x_samples);

drbenvincent

true_mean = 0;
true_sigma = 1;
% likelihood_func = @(x, mean, sigma) normpdf(x, mean, sigma);
% the above function to calcalate in matrix form, for speed
likelihood_func = @(x, mean, sigma)...
	prod(normpdf(repmat(x,[1 numel(mean)]),...
	repmat(mean, [1 numel(x)])',...
	repmat(sigma,[1 numel(x)])' ), 1);

%% generate data

drbenvincent

%% true probability distribution
true_func = @(x) betapdf(x,1+1,1+10);

%% Do rejection sampling
% create many samples on interval 0-1
x_samples = rand(10^6,1);
% evaluate for each sample
sample_value = true_func(x_samples);
% accept in proportion to highest
max_value = max(sample_value);