some drug test blog post

pk_trial.m

clear all; clc;
num_samples = 100;
x = linspace(0,1,101);

% First step - start from nothing and get an informative prior
alpha_uniform = 1;
beta_uniform = 1;
alpha_prior = 30;
beta_prior = 70;
failures_prior = 30;
alpha_info_prior = alpha_uniform + failures_prior;
beta_info_prior = beta_uniform + num_samples - failures_prior;
y_info_prior = pdf('beta', x, alpha_info_prior, beta_info_prior);
prob_info_prior = cdf('beta', x, alpha_info_prior, beta_info_prior);

% Using the previous posterior as a prior to get final posterior
alpha_likelihood = 17;
beta_likelihood = 83;
failures_posterior = 17;
alpha_posterior = alpha_info_prior + failures_posterior;
beta_posterior = beta_info_prior + num_samples - failures_posterior;
y_posterior = pdf('beta', x, alpha_posterior, beta_posterior);
prob_posterior = cdf('beta', x, alpha_posterior, beta_posterior);

figure
subplot(2,1,1)
plot(x,y_info_prior, x, y_posterior);
legend('Prior', 'Posterior');
subplot(2,1,2)
plot(x,prob_info_prior, x, prob_posterior);
legend('Prior', 'Posterior');