def point_2(fit, fit_summary):
posterior_tau_task_6 = fit.extract('tau')['tau']
task_6_mean = np.mean(posterior_tau_task_6)
task_6_hdi = hdi(posterior_tau_task_6)
posterior_tau_task_5 = pickle.load(
open('05-assignment/tau_posterior_for_assignment_6.pkl', 'rb'))['tau']
task_5_mean = np.mean(posterior_tau_task_5)
task_5_hdi = hdi(posterior_tau_task_5)
tau_diff = posterior_tau_task_6 - posterior_tau_task_5
diff_mean = np.mean(tau_diff)
diff_hdi = hdi(tau_diff)
diff_effect = tau_diff / np.std(tau_diff)
print(f'τ difference mean: {diff_mean:.2f}, HDI: {diff_hdi}')
print(
f'Effect on τ mean: {np.mean(diff_effect):.2f}, HDI: {hdi(diff_effect)}'
)
plt.figure()
plot_dist_mean_hdi(posterior_tau_task_6, color='b', label='Task 6')
plot_dist_mean_hdi(posterior_tau_task_5, color='r', label='Task 5')
plt.legend()
sns.despine(left=True)
plt.xlabel('Posterior τ')
plt.ylabel('Probability density')
plt.savefig('06-assignment/normal/posterior_tau_comparison.png')
def point_1(fit, fit_summary):
adult_posterior_mu = fit.extract('mu[1]')['mu[1]']
child_posterior_correction = fit.extract('mu[2]')['mu[2]']
child_posterior_mu = adult_posterior_mu + child_posterior_correction
adult_mean = np.mean(adult_posterior_mu)
child_mean = np.mean(child_posterior_mu)
diff_mean = np.mean(child_posterior_correction)
adult_hdi = hdi(adult_posterior_mu, 0.95)
child_hdi = hdi(child_posterior_mu, 0.95)
diff_hdi = hdi(child_posterior_correction, 0.95)
child_correction_effect_size = child_posterior_correction / np.std(child_posterior_correction)
print(f'Adult HDI: {adult_hdi}')
print(f'Child HDI: {child_hdi}')
print(f'Difference HDI: {diff_hdi}')
plt.figure()
sns.distplot(adult_posterior_mu, bins=20, norm_hist=True, label='Adult log posterior μ')
sns.distplot(child_posterior_mu, bins=20, norm_hist=True, label='Child log posterior μ')
plt.axvline(adult_mean, color='b', lw=2, label='Adult mean')
plt.axvline(adult_hdi[0], color='b', lw=2, linestyle='--', label='Adult 95% HDI')
plt.axvline(adult_hdi[1], color='b', lw=2, linestyle='--')
plt.axvline(child_mean, color='r', lw=2, label='Child mean')
plt.axvline(child_hdi[0], color='r', lw=2, linestyle='--', label='Child 95% HDI')
plt.axvline(child_hdi[1], color='r', lw=2, linestyle='--')
plt.legend()
sns.despine(left=True)
plt.xlabel('Posterior log reaction time')
plt.ylabel('Probability density')
plt.xlim(5.4, 6.4)
plt.savefig('06-assignment/student/posterior_log_reaction_times.png')
plt.figure()
sns.distplot(child_posterior_correction, bins=20, norm_hist=True, label='Posterior difference')
plt.axvline(diff_mean, color='b', lw=2, label='Difference mean')
plt.axvline(diff_hdi[0], color='b', lw=2, linestyle='--', label='Difference 95% HDI')
plt.axvline(diff_hdi[1], color='b', lw=2, linestyle='--')
plt.legend()
sns.despine(left=True)
plt.xlabel('Difference in posterior log reaction times')
plt.ylabel('Probability density')
plt.xlim(-0.1, 0.9)
plt.savefig('06-assignment/student/posterior_log_reaction_difference.png')
plt.figure()
plot_dist_mean_hdi(child_correction_effect_size, color='b', label='Effect size')
plt.legend()
sns.despine(left=True)
plt.xlabel('Effect size')
plt.ylabel('Probability density')
plt.xlim(-0.5, 9)
plt.savefig('06-assignment/student/effect_size.png')
def point_2(fit, summary, fit_model):
num_posterior_samples = (fit.sim['iter'] -
fit.sim['warmup']) * fit.sim['chains']
#random_new_person_index = np.random.randint(num_posterior_samples)
num_new_people = 10000
random_person_samples = np.zeros((num_new_people, ))
for i in range(num_new_people):
new_person_mu = fit.extract('mu')['mu'][np.random.randint(
num_posterior_samples)]
new_person_tau = fit.extract('tau')['tau'][np.random.randint(
num_posterior_samples)]
new_person_sigma = fit.extract('sigma')['sigma'][np.random.randint(
num_posterior_samples)]
new_person_theta = np.random.normal(new_person_mu, new_person_tau)
sample_log_reaction_times = np.random.normal(new_person_theta,
new_person_sigma, (1, ))
#sample_reaction_times = np.exp(sample_log_reaction_times)
random_person_samples[i] = np.exp(sample_log_reaction_times)
random_person_hdi = hdi(random_person_samples, 0.95)
print(
f'Expected value of randomly drawn people: {np.mean(random_person_samples):.2f}'
)
print(f'HDI of randomly drawn people samples: {random_person_hdi}')
plt.figure()
sns.distplot(random_person_samples, bins=20, norm_hist=True)
plt.plot(random_person_hdi, [0, 0], 'k', linewidth=5)
plt.savefig('05-assignment/point_2.png')
pickle.dump(np.log(random_person_samples),
open('05-assignment/random_person_samples.pkl', 'wb'))
def plot_dist_mean_hdi(data, label='', color='k'):
data_hdi = hdi(data)
sns.distplot(data, bins=20, norm_hist=True, label=f'{label} posterior')
plt.axvline(np.mean(data), color=color, lw=2, label=f'{label} mean')
plt.axvline(data_hdi[0],
color=color,
lw=2,
linestyle='--',
label=f'{label} 95% HDI')
plt.axvline(data_hdi[1], color=color, lw=2, linestyle='--')
def point_1(data):
model = load_stan_model('05-assignment/hierarchical_model.stan', True)
fit, summary, fit_model = fit_stan_model(model,
data,
iter=10000,
warmup=1000)
the_dude_posterior = fit.extract('exp_theta')['exp_theta'][:, 3]
mu_posterior = fit.extract('exp_mu')['exp_mu']
random_posteriors = fit.extract('exp_theta')['exp_theta'][:, [10, 1]]
sns.distplot(the_dude_posterior,
bins=30,
norm_hist=True,
label='The Dude θ')
sns.distplot(mu_posterior, bins=30, norm_hist=True, label='Group θ')
sns.distplot(random_posteriors[:, 0], bins=30, norm_hist=True)
sns.distplot(random_posteriors[:, 1], bins=30, norm_hist=True)
print(f'The Dude\'s mean: {np.mean(the_dude_posterior):.2f}')
print(f'The group mean: {np.mean(mu_posterior):.2f}')
plt.axvline(np.mean(the_dude_posterior),
color='b',
lw=2,
linestyle='--',
label='The Dude mean')
plt.axvline(np.mean(mu_posterior),
color='r',
lw=2,
linestyle='--',
label='Group mean')
the_dude_hdi = hdi(the_dude_posterior, 0.95)
mu_hdi = hdi(mu_posterior, 0.95)
print(f'The Dude\'s HDI: {the_dude_hdi}')
print(f'The group HDI: {mu_hdi}')
plt.legend()
sns.despine()
plt.savefig('05-assignment/point_1.png')
pickle.dump(fit.extract('tau'),
open('05-assignment/tau_posterior_for_assignment_6.pkl', 'wb'))
return fit, summary, fit_model
def point_2(fit, fit_summary):
posterior_tau_task_6 = fit.extract('tau')['tau']
task_6_mean = np.mean(posterior_tau_task_6)
task_6_hdi = hdi(posterior_tau_task_6)
posterior_tau_task_5 = pickle.load(open('05-assignment/tau_posterior_for_assignment_6.pkl', 'rb'))['tau']
task_5_mean = np.mean(posterior_tau_task_5)
task_5_hdi = hdi(posterior_tau_task_5)
tau_diff = posterior_tau_task_6 - posterior_tau_task_5
diff_mean = np.mean(tau_diff)
diff_hdi = hdi(tau_diff)
plt.figure()
plot_dist_mean_hdi(posterior_tau_task_6, color='b', label='Task 6')
plot_dist_mean_hdi(posterior_tau_task_5, color='r', label='Task 5')
plt.legend()
sns.despine(left=True)
plt.xlabel('Posterior τ')
plt.ylabel('Probability density')
plt.savefig('06-assignment/student/posterior_tau_comparison.png')
def point_2():
model = load_stan_model('04-assignment/model_3.stan')
y = [1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1]
z = [1, 0, 0, 0, 0, 0, 0, 1, 1, 0]
data_y = {'N': len(y), 'y': y}
data_z = {'N': len(z), 'y': z}
fit_y, summary_y, _ = fit_stan_model(model,
data_y,
iter=iterations,
seed=random_seed)
fit_z, summary_z, _ = fit_stan_model(model,
data_z,
iter=iterations,
seed=random_seed)
hdi_y = hdi(fit_y['theta'])
hdi_z = hdi(fit_z['theta'])
print(
f'Expected probability for getting heads with data y: {summary_y.loc["theta", "mean"]:.2f}'
)
print(f'HDI of y: {hdi_y[0]:.2f} - {hdi_y[1]:.2f}')
print(f'Probability of θ > 0.5: {np.mean(fit_y["theta"] > 0.5)}')
d_theta = fit_y['theta'] - fit_z['theta']
hdi_d_theta = hdi(d_theta)
probability_higher, point_of_even = compare_distributions(
fit_y['theta'], fit_z['theta'])
plt.figure()
sns.distplot(fit_y['theta'], bins=60, hist=True, label='θ_y')
sns.distplot(fit_z['theta'], bins=60, hist=True, label='θ_z')
plt.plot(hdi_y, [0, 0], 'b', alpha=0.5, linewidth=5, label='y 95% HDI')
plt.plot(hdi_z, [0, 0], 'r', alpha=0.5, linewidth=5, label='z 95% HDI')
plt.axvline(point_of_even, color='r', linestyle='--', alpha=0.5)
plt.xlabel('θ')
plt.ylabel('Density')
plt.legend()
plt.tight_layout()
sns.despine()
plt.savefig('04-assignment/comparison.png')
print(
f'Expected probability that y and z are drawn from the same coin: {1 - np.mean(d_theta > 0):.2f}'
)
print(
f'True positive rate of choosing coin y: {1 - probability_higher:.2f}')
print(
f'HDI of difference between y and z: {hdi_d_theta[0]:.2f} - {hdi_d_theta[1]:.2f}'
)
plt.figure()
sns.distplot(d_theta, hist=True)
plt.plot(hdi_d_theta, [0, 0], 'k', linewidth=5, label='95% HDI')
plt.xlabel('dθ')
plt.ylabel('Density')
plt.legend()
plt.tight_layout()
sns.despine()
plt.savefig('04-assignment/figure-point-2.png')
plt.show()