47 lines
1.5 KiB
Matlab
47 lines
1.5 KiB
Matlab
mu = 3.0;
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sigma =2.0;
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ns = [50, 1000];
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for k = 1:length(ns)
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n = ns(k);
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fprintf('\nn=%d\n', n);
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% draw random numbers:
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x = randn(n,1)*sigma+mu;
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datamean = mean(x);
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fprintf(' mean %.3f\n', datamean)
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% we assume the mean to be given, therefore dof=n:
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fprintf(' standard deviation %.3f\n', std(x, 1))
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% standard deviation as parameter:
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psigs = 1.0:0.001:3.0;
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% matrix with the probabilities for each x and psigs:
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lms = zeros(length(x), length(psigs));
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for i=1:length(psigs)
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psig = psigs(i);
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% same mean as for the standard deviation of the data:
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p = exp(-0.5*((x-datamean)/psig).^2.0)/sqrt(2.0*pi)/psig;
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lms(:,i) = p;
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end
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lm = prod(lms, 1); % likelihood
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loglm = sum(log(lms), 1); % log likelihood
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maxlm = psigs(lm==max(lm));
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if length(maxlm) > 1
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maxlm = maxlm(1);
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end
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maxloglm = psigs(loglm==max(loglm));
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fprintf(' likelihood: standard deviation %.3f\n', maxlm)
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fprintf(' log-likelihood: standard deviation %.3f\n', maxloglm)
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% plot likelihood of standard deviation:
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subplot(2, 2, 2*k-1);
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plot(psigs, lm );
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title(sprintf('likelihood n=%d', n));
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xlabel('standard deviation')
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ylabel('likelihood')
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subplot(2, 2, 2*k);
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plot(psigs, loglm);
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title(sprintf('log-likelihood n=%d', n));
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xlabel('standard deviation')
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ylabel('log likelihood')
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end
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savefigpdf(gcf, 'mlestd.pdf', 15, 10);
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