% Lecture 5A example: Normally distributed star brightness
%
% Numerical pointwise evaluation,
% without using the special normal-distribution formula

theta = linspace(0,10,1000);    % Try all these different theta values
pri   = normpdf(theta, 5, 1);
lik   = normpdf(3,theta,2) .* normpdf(8,theta,2) .* normpdf(7,theta,2);
unpost= pri .* lik;             % Pointwise multiplication
post  = unpost / sum(unpost);   % Normalization

clf
subplot(3,1,1)
plot(theta, pri)
grid on
title('prior for brightness')
subplot(3,1,2)
plot(theta, lik)
grid on
title('likelihood (from data 3,8,7)')
subplot(3,1,3)
plot(theta, post);
grid on
title('posterior for brightness')