Chapter 3: uninformed and informed uniform priors over gaussian parameters

d=[67 48 76]; n=length(d);% pmax=nan(n,1);

mus=linspace(0,100,501);

sigs=linspace(0,40,401); sigs=sigs(2:end);

mumin=0; mumax=100;

sigmin=0.5; sigmax=40;

primu=zeros(length(mus),1); primu(and(mus>=mumin,mus<=mumax))=1;

%sigs=sqrt(s2); %for punctate estimate

%prisig=1;

prisig=zeros(1,length(sigs)); prisig(and(sigs>=sigmin,sigs<=sigmax))=1;

pri=primu*prisig; pri=pri/sum(sum(pri));

avg=mean(d); s2=mean(d.^2)-avg^2;

like=@(muin,sigin) sigin^-n*exp(-n/2*(avg-muin)^2/sigin^2)*exp(-n/2*s2/sigin^2);

p=nan(length(mus),length(sigs)); %initialize posterior matrix

for mnow=1:length(mus),

for snow=1:length(sigs),

p(mnow,snow)=pri(mnow,snow)*like(mus(mnow),sigs(snow)); end, end

figure(1); meshc(sigs,mus,p); colormap bone

xlabel('sigma'); ylabel('mu'); zlabel('p');

figure(2);

subplot(2,1,1)

plot(sigs,sum(p,1)/sum(sum(p)),'k:','LineWidth',2)

xlabel('sigma'); ylabel('p')

subplot(2,1,2)

plot(mus,sum(p,2)/sum(sum(p)),'k:','LineWidth',2)

xlabel('mu'); ylabel('p')