Reorganized the folders and started a common script for the lectures.

statistics/code/bootstrapsem.m

@@ -1,24 +0,0 @@
-nsamples = 100;
-nresamples = 1000;
-
-% draw a SRS (simple random sample, "Stichprobe") from the population:
-x = randn( 1, nsamples );
-fprintf('%-30s  %-5s  %-5s  %-5s\n', '', 'mean', 'stdev', 'sem' )
-fprintf('%30s  %5.2f  %5.2f  %5.2f\n', 'single SRS', mean( x ), std( x ), std( x )/sqrt(nsamples) )
-
-% bootstrap the mean:
-mus = zeros(nresamples,1);  % vector for storing the means
-for i = 1:nresamples        % loop for generating the bootstraps
-    inx = randi(nsamples, 1, nsamples);  % range, 1D-vector, number
-    xr = x(inx);            % resample the original SRS
-    mus(i) = mean(xr);      % compute statistic of the resampled SRS
-end
-fprintf('%30s  %5.2f  %5.2f  -\n', 'bootstrapped distribution', mean( mus ), std( mus ) )
-
-% many SRS (we can do that with the random number generator, but not in real life!):
-musrs = zeros(nresamples,1);      % vector for the means of each SRS
-for i = 1:nresamples
-    x = randn( 1, nsamples );     % draw a new SRS
-    musrs(i) = mean( x );         % compute its mean
-end
-fprintf('%30s  %5.2f  %5.2f  -\n', 'sampling distribution', mean( musrs ), std( musrs ) )

statistics/code/lsq_error.m

@@ -1,6 +0,0 @@
-function error = lsq_error(parameter, x, y)
-% parameter(1) is the slope
-% parameter(2) is the intercept
-
-f_x = x .* parameter(1) + parameter(2);
-error = mean((f_x - y).^2);

statistics/code/lsq_gradient.m

@@ -1,7 +0,0 @@
-function gradient = lsq_gradient(parameter, x, y)
-h = 1e-6;
-
-partial_m = (lsq_error([parameter(1)+h, parameter(2)],x,y) - lsq_error(parameter,x,y))/ h;
-partial_n = (lsq_error([parameter(1), parameter(2)+h],x,y) - lsq_error(parameter,x,y))/ h;
-
-gradient = [partial_m, partial_n];

statistics/code/lsq_gradient_sigmoid.m

@@ -1,9 +0,0 @@
-function gradient = lsq_gradient_sigmoid(parameter, x, y)
-h = 1e-6;
-
-gradient = zeros(size(parameter));
-for i = 1:length(parameter)
-    parameter_h = parameter;
-    parameter_h(i) = parameter_h(i) + h;
-    gradient(i) = (lsq_sigmoid_error(parameter_h, x, y) - lsq_sigmoid_error(parameter, x, y)) / h;
-end

statistics/code/lsq_sigmoid_error.m

@@ -1,8 +0,0 @@
-function error = lsq_sigmoid_error(parameter, x, y)
-% p(1) the amplitude
-% p(2) the slope
-% p(3) the x-shift
-% p(4) the y-shift
-
-y_est = parameter(1)./(1+ exp(-parameter(2) .* (x - parameter(3)))) + parameter(4);
-error = mean((y_est - y).^2);

statistics/code/mlemean.m

@@ -1,29 +0,0 @@
-% draw random numbers:
-n = 100;
-mu = 3.0;
-sigma =2.0;
-x = randn(n,1)*sigma+mu;
-fprintf('              mean of the data is %.2f\n', mean(x))
-fprintf('standard deviation of the data is %.2f\n', std(x))
-
-% mean as parameter:
-pmus = 2.0:0.01:4.0;
-% matrix with the probabilities for each x and pmus:
-lms = zeros(length(x), length(pmus));
-for i=1:length(pmus)
-    pmu = pmus(i);
-    p = exp(-0.5*((x-pmu)/sigma).^2.0)/sqrt(2.0*pi)/sigma;
-    lms(:,i) = p;
-end
-lm = prod(lms, 1);          % likelihood
-loglm = sum(log(lms), 1);   % log likelihood
-
-% plot likelihood of mean:
-subplot(1, 2, 1);
-plot(pmus, lm );
-xlabel('mean')
-ylabel('likelihood')
-subplot(1, 2, 2);
-plot(pmus, loglm );
-xlabel('mean')
-ylabel('log likelihood')

statistics/code/plot_error_surface.m

@@ -1,112 +0,0 @@
-clear
-close all
-
-%% first, plot the raw data
-load('lin_regression.mat');
-
-figure()
-plot(x,y, 'o')
-xlabel('Input')
-ylabel('Output')
-
-%% plot the error surface
-clear
-load('lin_regression.mat')
-ms = -5:0.25:5;
-ns = -30:1:30;
-
-error_surf = zeros(length(ms), length(ns));
-
-for i = 1:length(ms)
-    for j = 1:length(ns)
-        error_surf(i,j) = lsq_error([ms(i), ns(j)], x, y);
-    end
-end
-
-
-% plot the error surface
-figure()
-[N,M] = meshgrid(ns, ms);
-s = surface(M,N,error_surf);
-xlabel('slope')
-ylabel('intercept')
-zlabel('error')
-view(3)
-% rotate(s, [1 1 0], 25 )
-
-%% Plot the gradient at different points in the surface
-clear
-load('lin_regression.mat')
-
-ms = -1:0.5:5;
-ns = -10:1:10;
-
-error_surf = zeros(length(ms), length(ns));
-gradient_m = zeros(size(error_surf));
-gradient_n = zeros(size(error_surf));
-
-for i = 1:length(ms)
-    for j = 1:length(ns)
-        error_surf(i,j) = lsq_error([ms(i), ns(j)], x, y);
-        grad = lsq_gradient([ms(i), ns(j)], x, y);
-        gradient_m(i,j) = grad(1);
-        gradient_n(i,j) = grad(2);
-    end
-end
-
-figure()
-hold on
-[N, M] = meshgrid(ns, ms);
-surface(M,N, error_surf, 'FaceAlpha', 0.5);
-contour(M,N, error_surf, 50);
-quiver(M,N, gradient_m, gradient_n)
-view(3)
-xlabel('slope')
-ylabel('intercept')
-zlabel('error')
-
-%% do the gradient descent
-clear 
-close all
-
-load('lin_regression.mat')
-
-ms = -1:0.5:5;
-ns = -10:1:10;
-
-position = [-2. 10.];
-gradient = [];
-error = [];
-eps = 0.01;
-
-% claculate error surface
-error_surf = zeros(length(ms), length(ns));
-for i = 1:length(ms)
-    for j = 1:length(ns)
-        error_surf(i,j) = lsq_error([ms(i), ns(j)], x, y);
-    end
-end
-figure()
-hold on
-[N, M] = meshgrid(ns, ms);
-surface(M,N, error_surf, 'FaceAlpha', 0.5);
-view(3)
-xlabel('slope')
-ylabel('intersection')
-zlabel('error')
-
-% do the descent
-
-while isempty(gradient) || norm(gradient) > 0.1
-    gradient = lsq_gradient(position, x,y);
-    error = lsq_error(position, x, y);
-    plot3(position(1), position(2), error, 'o', 'color', 'red')
-    position = position - eps .* gradient; 
-    pause(0.25)
-end
-disp('gradient descent done!')
-disp(strcat('final position: ', num2str(position)))
-disp(strcat('final error: ', num2str(error)))
-
-
-

statistics/code/sigmoidal_gradient_descent.m

@@ -1,44 +0,0 @@
-
-
-%% fit the sigmoid
-
-clear 
-close all
-
-load('iv_curve.mat')
-
-figure()
-plot(voltage, current, 'o')
-xlabel('voltate [mV]')
-ylabel('current [pA]')
-
-% amplitude, slope, x-shift, y-shift
-%parameter = [10 0.25 -50, 2.5];
-parameter = [20 0.5 -50, 2.5];
-
-eps = 0.1;
-% do the descent
-gradient = [];
-steps = 0;
-error = [];
-
-while isempty(gradient) || norm(gradient) > 0.01
-    steps = steps + 1; 
-    gradient = lsq_gradient_sigmoid(parameter, voltage, current);
-    error(steps) = lsq_sigmoid_error(parameter, voltage, current);
-    parameter = parameter - eps .* gradient; 
-end
-plot(1:steps, error)
-
-disp('gradient descent done!')
-disp(strcat('final position: ', num2str(parameter)))
-disp(strcat('final error: ', num2str(error(end))))
-
-%% use fminsearch
-parameter = [10 0.5 -50, 2.5];
-
-objective_function = @(p)lsq_sigmoid_error(p, voltage, current);
-param = fminunc(objective_function, parameter);
-disp(param)
-param1 = fminsearch(objective_function, parameter);
-disp(param1)