def test_beta_approx_1d(self):
x0 = np.array([0.9])
true_dist = beta(1000, 1000)
approx = approx_dist(true_dist.logpdf, x0)
self.assertAlmostEqual(float(approx.mean[0]), true_dist.mean())
self.assertAlmostEqual(float(approx.cov[0]),
true_dist.var(),
delta=1e-5)
def test_binomial_observation_posterior(self):
x0 = np.array([0.25])
def posterior_logpdf(v):
if 0 < v < 1:
return binom.logpmf(2000, 3000, v)
return -np.inf
approx = approx_dist(posterior_logpdf, x0)
true_dist = beta(2001, 1001)
self.assertAlmostEqual(float(approx.mean[0]),
true_dist.mean(),
delta=1e-3)
self.assertAlmostEqual(float(approx.cov[0]),
true_dist.var(),
delta=1e-5)
def test_linear_regression_posterior(self):
def lin_regression_lnprob(v, x=None, y=None):
a, b, s = v
if s <= 0:
return -np.inf
y_hat = a + b * x
lp = np.sum(norm.logpdf(y, y_hat, s))
return lp
x = np.linspace(0, 5000, 1000)
y = 5 - 10 * x + np.random.normal(0, 2, 1000)
L = partial(lin_regression_lnprob, x=x, y=y)
approx = approx_dist(L, np.array([0, 0, 1]))
self.assertAlmostEqual(float(approx.mean[0]), 5, delta=1e-1)
self.assertAlmostEqual(float(approx.mean[1]), -10, delta=1e-1)
self.assertAlmostEqual(float(approx.mean[2]), 2, delta=1e-1)
a, b, s = v
if s <= 0:
return -np.inf
y_hat = a + b * x
lp = np.sum(norm.logpdf(y, y_hat, s))
return lp
TRUE_A = 0.1
TRUE_B = -10
TRUE_S = 1.3
x = np.linspace(0, 1, 10000)
y = TRUE_A + TRUE_B * x + np.random.normal(0, TRUE_S, 10000)
L = partial(lin_regression_lnprob, x=x, y=y)
result = approx_dist(L, np.array([0, 0, 1]))
samples = result.rvs(1000)
plt.scatter(samples[:, 0], samples[:, 1], alpha=0.1)
plt.scatter([np.mean(samples[:, 0])], [np.mean(samples[:, 1])],
marker='x',
color='red',
label='Posterior mean')
plt.title('Posterior samples for intercept and coefficient of linear model')
plt.xlabel('Intercept')
plt.ylabel('Coefficient')
plt.axvline(TRUE_A, color='orange', label='True intercept')
plt.axhline(TRUE_B, label='True Coefficient')
plt.legend()
plt.show()
sns.distplot(samples[:, 2])
def test_norm_approx_1d(self):
x0 = np.array([1])
true_dist = norm(0, 1)
approx = approx_dist(true_dist.logpdf, x0)
self.assertAlmostEqual(float(approx.mean[0]), 0)
self.assertAlmostEqual(float(approx.cov[0]), 1)