Figures.m

% Generate Figures for paper
% Witkovsky V. and Wimmer G.: Confidence intervals for the location
% parameter based on digitized measurements. Mathematica Slovaca 2008,
% Submitted.
% Viktor Witkovsky ([e-mail])
% Revised: 02-May-2008 14:17:52

%% Figure 1
n = cell(4,1);
v = cell(4,1);
n{1} = 3;
n{2} = 5;
n{3} = 10;
n{4} = 1000;
obs = cell(4,1);
obs{1} = 0;
obs{2} = 0;
obs{3} = 0;
obs{4} = 0;
v{1} = [-3 3 0 5];
v{2} = [-1 1 0 2];
v{3} = [-0.7 0.7 0 0.8];
v{4} = [-0.5 0.5 0 0.2];

options = DigitFD;
options.sampleSize = 5000;

y = cell(4,1);
y{1} =  MeasuermentsFromCounts(obs{1},n{1});
y{2} =  MeasuermentsFromCounts(obs{2},n{2});
y{3} =  MeasuermentsFromCounts(obs{3},n{3});
y{4} =  MeasuermentsFromCounts(obs{4},n{4});

result = cell(4,1);

nmesh = 100;

for i = 1:4
subplot(2,2,i)
result{i} = DigitFD(y{i},options);
hold
u = v{i};
[X,Y] = meshgrid(u(1):(u(2)-u(1))/nmesh:u(2),u(3):(u(4)-u(3))/nmesh:u(4));
logLik = LogLik([X(:) Y(:)],y{i},1);
Z = reshape(logLik,nmesh+1,nmesh+1);
q = result{i}.LogLikelihoodQuantile;
contour(X,Y,Z,[q,q],'k')
hold
title(['Sample from Fiducial Distribution of (\mu,\sigma)\newline',...
    'Observed value: ',num2str(obs{i}),', n = ',num2str(n{i}),''])
axis(v{i})
end

print -depsc figure01.eps

%% Figure2

n = cell(4,1);
n{1} = [1 9];
n{2} = [5 5];
n{3} = [29 1];
n{4} = [15 15];
obs = cell(4,1);
obs{1} = [0 1];
obs{2} = [0 1];
obs{3} = [0 1];
obs{4} = [0 1];
v = cell(4,1);
v{1} = [0.2 1.6 0 1.2];
v{2} = [-0.5 1.5 0 1.8];
v{3} = [-0.3 0.5 0 0.5];
v{4} = [0.1 0.9 0 1];

options = DigitFD;
options.sampleSize = 5000;

y = cell(4,1);
y{1} =  MeasuermentsFromCounts(obs{1},n{1});
y{2} =  MeasuermentsFromCounts(obs{2},n{2});
y{3} =  MeasuermentsFromCounts(obs{3},n{3});
y{4} =  MeasuermentsFromCounts(obs{4},n{4});

result = cell(4,1);

for i = 1:4
subplot(2,2,i)
result{i} = DigitFD(y{i},options);
hold
u = v{i};
[X,Y] = meshgrid(u(1):(u(2)-u(1))/nmesh:u(2),u(3):(u(4)-u(3))/nmesh:u(4));
logLik = LogLik([X(:) Y(:)],y{i},1);
Z = reshape(logLik,nmesh+1,nmesh+1);
q = result{i}.LogLikelihoodQuantile;
contour(X,Y,Z,[q,q],'k')
hold
title(['Sample from Fiducial Distribution of (\mu,\sigma)\newline',...
    'Observed values: [',num2str(obs{i}),'], n = [',num2str(n{i}),']'])
axis(v{i})
end

print -depsc figure02.eps

%% Figure3

n = cell(4,1);
n{1} = [1 8 1];
n{2} = [1 6 4];
n{3} = [1 4 20 4 1];
n{4} = [1 2 18 7 2];
obs = cell(4,1);
obs{1} = [-1 0 1];
obs{2} = [-1 0 1];
obs{3} = [-2 -1 0 1 2];
obs{4} = [-2 -1 0 1 2];
v = cell(4,1);
v{1} = [-1 1.5 0 2];
v{2} = [-1 1.5 0 2];
v{3} = [-0.8 1 0.4 1.6];
v{4} = [-0.8 1 0.4 1.6];

options = DigitFD;
options.sampleSize = 5000;

y = cell(4,1);
y{1} =  MeasuermentsFromCounts(obs{1},n{1});
y{2} =  MeasuermentsFromCounts(obs{2},n{2});
y{3} =  MeasuermentsFromCounts(obs{3},n{3});
y{4} =  MeasuermentsFromCounts(obs{4},n{4});

result = cell(4,1);

for i = 1:4
subplot(2,2,i)
result{i} = DigitFD(y{i},options);
hold
u = v{i};
[X,Y] = meshgrid(u(1):(u(2)-u(1))/nmesh:u(2),u(3):(u(4)-u(3))/nmesh:u(4));
logLik = LogLik([X(:) Y(:)],y{i},1);
Z = reshape(logLik,nmesh+1,nmesh+1);
q = result{i}.LogLikelihoodQuantile;
contour(X,Y,Z,[q,q],'k')
hold
title(['Sample from Fiducial Distribution of (\mu,\sigma)\newline',...
    'Observed values: [',num2str(obs{i}),'], n = [',num2str(n{i}),']'])
axis(v{i})
end

print -depsc figure03.eps

%% Figure Example

measurements = [zeros(99,1),1];

options = DigitFD;
options.sampleSize = 5000;
options.beta = [0.05 0.001 0.1 0.2 0.3 0.4 0.5];
nmesh = 100;

result = DigitFD(measurements,options);
hold
v = axis;
%v = [-1 1 0 1.5];
u = v;
[X,Y] = meshgrid(u(1):(u(2)-u(1))/nmesh:u(2),u(3):(u(4)-u(3))/nmesh:u(4));
logLik = LogLik([X(:) Y(:)],y,1);
Z = reshape(logLik,nmesh+1,nmesh+1);
q = result.LogLikelihoodQuantile;
contour(X,Y,Z,q)
hold
title('Sample from Fiducial Distribution of (\mu,\sigma)')
axis(v)

%print -depsc figure.eps