Chapter 3: reparameterized scale parameters

The posteriors produced by reparameterization are shown as dashed blue lines in Fig. 3.5a, and are obtained from the Matlab code:

%Fig 1 (SD units)

piV=ones(size(Vs)); %uniform prior over variances

sdTX=@(x) sqrt(x); %linking function for transformation into SD units

PIsdTX=pTX(Vs,piV,sdTX); %transformation of uniform var prior; now SD

POsdTX=PIsdTX(:,1)'.*exp(-N/2*(mean(d.^2)-mean(d)^2)./SDs.^2).*SDs.^-N;

figure(1); plot(SDs,POsdTX/max(POsdTX),'b--','LineWidth',2.4)

%Fig 2 (variance units)

piSD=ones(size(SDs)); %uniform prior over SDs

vTX=@(x) x.^2; %linking function for transformation into var units

PIvTX=pTX(SDs,piSD,vTX); %transformation of uniform SD prior; now var

POvTX=PIvTX(:,1)'.*exp(-N/2*(mean(d.^2)-mean(d)^2)./SDs.^2).*SDs.^(-N);

figure(2); plot(Vs,POvTX/max(POvTX),'b--','LineWidth',2.4)