Abstract
For the linear discrimination of two stimuli in white Gaussian noise in the presence of internal noise, a method is described for estimating linear classification weights from the sum of noise images segregated by stimulus and response. The recommended method for combining the two response images for the same stimulus is to difference the average images. Weights are derived for combining images over stimuli and observers. Methods for estimating the level of internal noise are described with emphasis on the case of repeated presentations of the same noise sample. Simple tests for particular hypotheses about the weights are shown based on observer agreement with a noiseless version of the hypothesis.
2 Template Estimation for Linear Classification of Two Signals in Additive White Gaussian Noise
The following is a MatLab program for calculating the example illustrated in
Figure 3.
% calculations shown only for 2 cpd data
pCS02 = [911 417 149 180 352 941];
pCS16 = [1290 552 115 370 657 1016];
pfa =(pCS(3)+0.5*pCS(2))/... (pCS(3)+pCS(2)+pCS2(1)); 0.2420; pht = (pCS(6)+0.5*pCS(5))/... (pCS(6)+pCS(5)+pCS(4)); 0.7583;
dH = znorm(pht)−znorm(pfa);1.4006;
d0 = 3.2006;% stimulus snr
nPairs(1)=(pCS(3)+pCS(2)+pCS(1)); 1477
nPairs(2)=(pCS(6)+pCS(5)+pCS(4)); 1473
sameProp(1)=(pCS(1)+pCS(3))/nPairs(1); 0.7177
sameProp(2)=(pCS(4)+pCS(6))/nPairs(2); 0.7610
confIntProp=1.96*sqrt((p−p*p)/n);
confInterval(s,:)=[p, p−confIntProp, p+confIntProp];
[0.7177 0.6947 0.7406 0.7610 0.7393 0.7828];
% solve for internal noise from psame, c, m
n = 25;% integration approx. parameter
f=inline(‘(psame-probSame(si,c,m,n,range))^2’,... ‘si’,‘psame’,‘c’,‘m’,‘n’,‘range’);
×1=0.001;% zero won’t work
ms= [0.0 dH];% no signal, signal
sfinal(s,i)=fminbnd(f, x1,x2,
[0.3904 0.2931 0.4819 0.5564 0.4755 0.6313];
[0.2942 0.1938 0.3880 0.4462 0.3811 0.5087];
plot(1,se202(1,1),‘ko’,[1 1],se202(1,2:3),‘k.-’,...
3,se202(2,1),‘ko’,[3 3],se202(2,2:3),‘k.-’,...
5,se216(1,1),‘ko’,[5 5],se216(1,2:3),‘k.-’,...
7,se216(2,1),‘ko’,[7 7],se216(1,2:3),‘k.-’,...
function prob=probSame(si,c,m,n,range)
% Prob(same) from si, c, m
p=(p.*(1.−p)).*exp(−0.5.*s.*s);
prob=1.0–2.0*sum(p)/(n*sqrt(2*pi));