bernoulliBetaSequentialUpdate.m

%% Sequential Bayesian Updating of a Beta-Bernoulli model. 
% In this example we draw samples from a Bernoulli distribution and then
% sequentially fit a Beta-Bernoulli model, plotting the posterior of the
% parameters at each iteration. 
%% Sample

% This file is from pmtk3.googlecode.com

setSeed(0);
mu = 0.7;  % 70% probability of success
n  = 100;  % number of samples 
X  = rand(n, 1) < mu;
%% Update & Plot
figure; hold on; box on;
[styles, colors, symbols] =  plotColors();
ns = [5 50 100];        
betaPrior = [0.5, 0.5]; % uninformative prior
xs = linspace(0.001, 0.999, 40); 
model = struct(); 
for i=1:numel(ns)
    n = ns(i);
    Xsubset = X(1:n);
    nsucc   = sum( Xsubset);
    nfail   = sum(~Xsubset);
    model.a = betaPrior(1) + nsucc;
    model.b = betaPrior(2) + nfail;
    p = exp(betaLogprob(model, xs));
    name = sprintf('n=%d', n);
    plot(xs, p, [styles{i}, colors(i)], 'LineWidth', 3, 'DisplayName', name);
end
axis([0, 1, -0.2, 10.5])
h = verticalLine(mean(X), 'LineStyle'  , '--'    , ...
                          'LineWidth'  , 2.5     , ...
                          'Color'      , 'c'     , ...
                          'DisplayName', 'truth' );
if ~isOctave
    uistack(h, 'bottom');
end
legend('Location', 'NorthWest');
printPmtkFigure betaSeqUpdate