Chapter 4: gaussian prior predictive and sampling

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%%% Gaussian Prior Predictive (F4.3) %%%

Nx=300; Nm=200;

Mlist=linspace(-20,20,Nm)'*ones(1,Nx); Slist=3; xlist=ones(Nm,1)*linspace(-15,15,Nx);

%%% F4.1a %%%

Lnow=-log(Slist)-.5*log(2*pi)-.5*(Mlist-xlist).^2/Slist^2;

figure(5); clf; mesh(xlist(1,:),Mlist(:,1),exp(Lnow)); view(-61,48.5)

xlabel('x (data)','FontName','Arial','FontSize',13)

ylabel('\mu (parameter)','FontName','Arial','FontSize',13)

zlabel('p','FontName','Arial','FontSize',13)

%%% F4.1b %%%

pri=zeros(size(Mlist(:,1)))-log(diff(Mlist([1 end])));

figure(6); clf; plot(Mlist(:,1),exp(pri),'ko','MarkerFaceColor','k','MarkerSize',8); r=axis; axis([r(1:2) 0 .03]); box off

xlabel('\mu (parameter)','FontName','Arial','FontSize',13)

ylabel('p','FontName','Arial','FontSize',13)

%%% F4.1c %%%

Lnow=logsum(Lnow+pri*ones(1,Nx)+log(diff(Mlist(1:2,1))),1);

figure(7); clf; plot(xlist(1,:),exp(Lnow),'ko','MarkerFaceColor','k','MarkerSize',8);

box off; axis([min(min(xlist))-.5 max(max(xlist))+.5 0 1.04*max(exp(Lnow))])

ylabel('p','FontName','Arial','FontSize',13)

xlabel('x (data)','FontName','Arial','FontSize',13)

%%% F4.1d %%%

N=101; %sig=Slist; mu=0;

cumpdrawn=rand(N,1);

tevald=xlist(1,:);

cumpevald=cumsum(exp(Lnow));

cumind=nan(N,1);

for nbr=1:N, cumind(nbr)=findnearestN(cumpevald,cumpdrawn(nbr),1); end

Gdraw=tevald(cumind);

figure(8); clf; hold on

[N X]=hist(Gdraw,51);

bar(X,N,'FaceColor',.25*[1 1 1])

box off; axis([min(tevald) max(tevald) 0 10])

xlabel('x (location)','FontName','Arial','FontSize',13)