Chapter 5: body temperature measurement

This is the most common problem in all of measurement, with a constant signal and constant noise. We start with the data, which involves one or more observations of thermometer mercury level.

d=[98.4 98.8 98.5 99.4 99.9];

mus=linspace(90,110,3001)';

sigmas=linspace(0,20,501); sigmas=sigmas(2:end);

N=length(d);

%%% 2d mu-sigma distribution

Lms=-(N/2*((mean(d.^2)-mean(d)^2)*(sigmas.^-2)+(mus-mean(d)).^2*(sigmas.^-2))+(N+1)*ones(size(mus))*log(sigmas));

figure; meshc(sigmas,mus,exp(Lms)); colormap bone

%%% marginal alpha distribution

Lm=logsum(Lms,2,diff(sigmas(1:2))); Lm=Lm-max(Lm);

ciM=CIp(mus,Lm);

%%% marginal sigma distribution

Ls=logsum(Lms,1,diff(mus(1:2))); Ls=Ls-max(Ls);

ciS=CIp(sigmas(:),Ls);

figure

%%% plot marginal alpha distribution

subplot(2,1,1); hold on

plot(mus,exp(Lm),'k--','LineWidth',1.75); dciM=diff(ciM(1:2)); axis([ciM(1)-.2*dciM ciM(2)+.2*dciM 0 1])

for n=1:2, plot(ciM(n)*[1 1],[0 1],'-','Color',.65*[1 1 1],'LineWidth',.7); end

%%% plot marginal sigma distribution

subplot(2,1,2); hold on

plot(sigmas,exp(Ls),'k--','LineWidth',1.75); dciS=diff(ciS(1:2)); axis([ciS(1)-.2*dciS ciS(2)+.2*dciS 0 1])

for n=1:2, plot(ciS(n)*[1 1],[0 1],'-','Color',.65*[1 1 1],'LineWidth',.7); end