gaussInferParamsMean1d.m

%% Infer the mean of a 1D Gaussian
%
%%

% This file is from pmtk3.googlecode.com

priorVar = [1 5];
Sigma = 1; % Assumed to be known
figstr = {'gaussStrongPrior', 'gaussWeakPrior'};
X = 3; % data
[styles, colors, symbols, plotstyle] =  plotColors();
figure; 
for i=1:numel(priorVar)
    %%
    prior.Sigma = priorVar(i);
    prior.mu    = 0;
    %%
    xbar = mean(X);
    n    = numel(X);
    %%
    lik.Sigma = Sigma;
    lik.mu    = xbar;
    %%
    S0    = prior.Sigma;
    S0inv = 1./S0;
    mu0   = prior.mu;
    S     = Sigma;
    Sinv  = 1./S;
    Sn    = 1./(S0inv + n*Sinv);
    %%
    post.mu    = Sn*(n*Sinv*xbar + S0inv*mu0);
    post.Sigma = Sn;
    %% Now plot
    %figure;  
    subplot(1,2,i)
    hold on
    xrange = -5:0.25:5;
    ms = 10; lw = 3;
    style = [styles{1}, symbols(1), colors(1)];
    plot(xrange, exp(gaussLogprob(prior, xrange)), plotstyle{1}, ...
        'displayname', 'prior', ...
        'linewidth'  , lw, 'markersize', ms);
    style = [styles{2}, symbols(2), colors(2)];
    plot(xrange, exp(gaussLogprob(lik  , xrange)), plotstyle{2}, ...
        'displayname', 'lik', ...
        'linewidth'  , lw, 'markersize', ms);
    style = [styles{3}, symbols(3), colors(3)];
    plot(xrange, exp(gaussLogprob(post , xrange)), plotstyle{3}, ...
        'displayname', 'post', ...
        'linewidth'  , lw, 'markersize', ms);
    set(gca, 'ylim', [0, 0.7]);
    legend('Location','NorthWest');
    title(sprintf('prior variance = %3.2f', priorVar(i)));
    box on;
    %printPmtkFigure(figstr{i});
end
printPmtkFigure('gaussInferParamsMean1d');