Chapter 6: zero-slope model evidence

Evidence for the zero-slope model depends on the orientation of the dataset relative to the horizontal axis.

clear %#ok<*UNRCH>

saveFLAG=0; plotFLAG=1;

COL=[.55*[1 1 1]; .3 .4 .85; .8 .5 .4];

N=6; sig=5; Ns=1201;

slist=linspace(0,101,Ns+1)'; slist=slist(2:end); %noise level

diffs=[diff(slist(1:2))]; thetas=linspace(-100,100,N);

Nrot=11; rotlist=linspace(-pi/12,pi/4+pi/12,Nrot);

%keep noise samples identical across simulations for clearer comparison

eorig=nrand(0,sig,[1 N]);

dorig=[thetas(:) zeros(N,1)];

margL=nan(Nrot,2); sest=zeros(Nrot,2);

for irot=1:Nrot, rotnow=rotlist(irot);

%%%%%%%%R%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% DATA SIM using rotation ratio %%%

dnow=rot(dorig,rotnow);

tnow=dnow(:,1)'; dnow=dnow(:,2)'+eorig;

likeFN0=-(N/2)*(mean( dnow.^2,2)./slist.^2)-(N+1)*log(slist); %output is Ns x 1

likeFN1=-(N/2)*(mean((dnow-tnow).^2,2)./slist.^2)-(N+1)*log(slist); %output is Ns x 1

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% param likelihood by condition %%%

Lall0=likeFN0;

Lall1=likeFN1;

%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% verify global sigma %%%

sest(irot,1)=logpeakval([Lall0 slist]);

sest(irot,2)=logpeakval([Lall1 slist]);

%%%%%%%%%%%%%%%%%%%%%%%%%

%%% Model likelihoods %%%

margL(irot,1)=logsum(Lall0,1,diffs);

margL(irot,2)=logsum(Lall1,1,diffs); end

Elist=10*(margL(:,2)-margL(:,1));

if plotFLAG,

figure(1); clf; hold on

plot(tan(rotlist),Elist,'ko-','MarkerFaceColor','k','MarkerSize',11);

xlabel('data slope','FontName','Arial','FontSize',15);

ylabel('evidence (db)','FontName','Arial','FontSize',15);

if saveFLAG, saveas(figure(1),['slmEvid.pdf']); end

figure(2); clf; hold on;

plot(tan(rotlist),margL(:,1),'ko:','MarkerFaceColor','k');

plot(tan(rotlist),margL(:,2),'ko:','MarkerFaceColor',COL(1,:))

xlabel('data slope','FontName','Arial','FontSize',15);

ylabel('mod likelihood','FontName','Arial','FontSize',15);

if saveFLAG, saveas(figure(30),['slmMLike.pdf']); end, end