Now we will use Python to compute and plot the posterior distribution based on the analytical expression we have just derived. In the following code, you will see there is actually one line that computes the results while the others are there just to get a nice plot:
plt.figure(figsize=(10, 8))n_trials = [0, 1, 2, 3, 4, 8, 16, 32, 50, 150]data = [0, 1, 1, 1, 1, 4, 6, 9, 13, 48]theta_real = 0.35beta_params = [(1, 1), (20, 20), (1, 4)]dist = stats.betax = np.linspace(0, 1, 200)for idx, N in enumerate(n_trials): if idx == 0: plt.subplot(4, 3, 2) plt.xlabel('θ') else: plt.subplot(4, 3, idx+3) plt.xticks([]) y = data[idx] for (a_prior, b_prior) in beta_params: p_theta_given_y = dist.pdf(x, a_prior + y, b_prior ...
