Chapter 5: straight-line model i

We first consider the straight-line model describing the mapping between auditory and physical space using a uniform prior over slope for a linear model written in slope-intercept form (s = mx+ b)

%set constants

SD=5; buzzers=-45:15:45; Nb=length(buzzers);

alpha=2; beta=.88;

alphas=linspace(-12,12,201); betas=linspace(0,2,501); sds=linspace(0,10,201);

dvec=alpha+beta*buzzers'+nrand(0,SD,[Nb 1]);

L=@(alphanow,sdnow) -(Nb+1)*sdnow-.5*sum((dvec*ones(size(betas))-(alphanow+buzzers'*betas)).^2)/sdnow^2;

%main loop (uniform beta prior)

postmat=zeros(length(betas),length(alphas),length(sds)); %initialize posterior mnatrix

for na=1:length(alphas),

for ns=1:length(sds),

postmat(:,na,ns)=L(alphas(na),sds(ns)); end, end

Bpost=logsum(postmat,[2 3],[diff(alphas(1:2)) diff(sds(1:2))]);

Apost=logsum(postmat,[1 3],[diff(betas(1:2)) diff(sds(1:2))]);

SDpost=logsum(postmat,[1 2],[diff(betas(1:2)) diff(alphas(1:2))]);

figure(2); clf

subplot(2,1,1); plot(betas,exp(Bpost-max(Bpost)),'k-','LineWidth',1.4); axis([0 2 0 1.02]); box off

subplot(2,1,2); plot(alphas,exp(Apost-max(Apost)),'k-','LineWidth',1.4); axis([-10 10 0 1.02]); box off