neymanPearson2.m

%% Illustration of the Neyman-Pearson testing paradigm
%
%%

% This file is from pmtk3.googlecode.com


xmin = -4;xmax = 8;
ymin = 0;ymax = 0.3;
res = 0.01;
domain = xmin:res:xmax;
sigma = 1.5;
f1 = @(x)gaussProb(x,0,sigma^2)';
f2 = @(x)gaussProb(x,4,sigma^2)';

linesize = {'LineWidth',2.5};
plot(domain,f1(domain),'-b',linesize{:});
hold on;
plot(domain,f2(domain),'-r',linesize{:});

axis([xmin,xmax,ymin,ymax]);
plot([2.3;2.3],[0;0.5],'-k',linesize{:});

left = find(domain == 2.25);
lineRes = 0.005;
xrange = xmin:lineRes:xmax;
xIntersectIdx = argmin(abs(xrange - 2.3));
upperEnd = max(f2(1:xIntersectIdx));
yrange = 0:lineRes:max(f2(xrange(1:xIntersectIdx)));
ypoints = [yrange; yrange];
offset = 0.17; 
xpoints = [gaussinv(yrange, 4, sigma.^2) - offset; 
           xrange(xIntersectIdx)*ones(1, length(yrange))];
line(xpoints, ypoints, 'Color', 'r'); 

lineRes = 0.1;
xrange = xmin:lineRes:xmax;
xIntersectIdx = find(xrange == 2.3);
xpoints = [xrange((xIntersectIdx+1):end); xrange((xIntersectIdx+1):end)];
ypoints = [zeros(1, length(xrange) - xIntersectIdx); f1(xrange((xIntersectIdx+1):end))];
line(xpoints, ypoints, 'Color', 'b'); 

set(gca,'XTick',2.3,'YTick',[],'XTickLabel',{'X*'},'FontSize',18);

annotation(gcf,'textarrow',rel2absX([0.5,1.9]),rel2absY([0.075,0.02]),...
    'TextEdgeColor','none',...
    'TextLineWidth',2,...
    'FontSize',20,...
    'String',{'\beta'},...
    'LineWidth',2);

annotation(gcf,'textarrow',rel2absX([4.1,2.6]),rel2absY([0.075,0.02]),...
    'TextEdgeColor','none',...
    'TextLineWidth',2,...
    'FontSize',20,...
    'String',{'\alpha'},...
    'LineWidth',2);

annotation(gcf,'textbox',[rel2absX(-0.4) rel2absY(0.275) 0.0403 0.07213],'String',{'H_0'},...
    'FontSize',16,...
    'FitBoxToText','off',...
    'LineStyle','none');

annotation(gcf,'textbox',[rel2absX(3.6) rel2absY(0.275) 0.0403 0.07213],...
    'String',{'H_1'},...
    'FontSize',16,...
    'FitBoxToText','off',...
    'LineStyle','none');