Sequential Bayesian Updating of a Bernoulli-Beta model.

In this example we draw samples from a BernoulliDist and then sequentially fit a Bernoulli_BetaDist model, plotting the posterior of the parameters at each iteration.

Contents

%#testPMTK

Sample

setSeed(0);
m = BernoulliDist('mu',0.7);        % 70% probability of success
n = 100;
X = sample(m, n);

Update & Plot

figure; hold on;
[styles, colors, symbols] =  plotColors();
ns = [0 5 50 100];
legendstr = cell(length(ns)+1,1);
for i=1:length(ns)
    n = ns(i);
    mm = Bernoulli_BetaDist('prior',BetaDist(0.5,0.5));
    mm = fit(mm, 'data', X(1:n));
    plot(mm.muDist, 'plotArgs', {styles{i}, 'linewidth', 2});
    legendstr{i} = sprintf('n=%d', n);
end
box on;
xbar = mean(X);
pmax = 10;
h=line([xbar xbar], [0 pmax]); set(h, 'linewidth', 3,'Color','c');
legendstr{length(ns)+1} = 'truth';
legend(legendstr,'Location','NorthWest');

Published with MATLAB® 7.7