% hw5a.m
% hw5, question 1: logit model via discretization

% note: calls the function stdn_cdf.m to calculate standard normal cdf

load hw5.mat
alpha = (-10):.1:10;
beta = 0:.01:.50;
K = length(alpha);
L = length(beta);
Posterior1 = zeros(K,L);
Posterior2 = zeros(K,L);
for k=1:K,
    for l=1:L,
        a = alpha(k);
        b = beta(l);
        r = stdn_cdf(a+b*x);
        f = prod((r.^y).*((1-r).^(1-y)));
        Posterior1(k,l) = f;
        Posterior2(k,l) = f * exp(-.5*100*(b^2));
    end;
end;

Posterior1 = Posterior1./(sum(sum(Posterior1)));
Posterior2 = Posterior2./(sum(sum(Posterior2)));

% calculate marginal posteriors for beta
PB1 = sum(Posterior1);
PB2 = sum(Posterior2);

plot(beta,[PB1' PB2'] )

% end hw5a.m