Chapter 6: evidence based on a truncated range of possible rate parameters

In the previous example, we demonstrated numerical calculation of the model likelihood when the model allowed the full range of possible rate parameters (i.e., the possible rates spanned the full binomial range, [0,1]). Here we will numerically compute the likelihood for both a model that uses a uniform and one that uses an exponential prior range, both now over only half the binomial range.

%%% prelim

N=40; S=14; thetas=linspace(0,.5,1201); theta2=0.5;

like2=bpdf(S,N,theta2);

EV=nan(1,2);

%%% numerical solution for Fig. 6.6b,upper

pri=2*ones(size(thetas));

like1=trapz(thetas,pri.*bpdf(S,N,thetas));

EV(1)=10*(log10(like1)-log10(like2));

%%% numerical solution for Fig. 6.6b,lower

lambda=-7.187; Tmax=.5;

pri=lambda.*exp(-lambda.*thetas)./(1-exp(-lambda.*Tmax));

like1=trapz(thetas,pri.*bpdf(S,N,thetas));

EV(2)=10*(log10(like1)-log10(like2));

%%% compare the two calculations

EV