def test_hamiltonian_monte_carlo():
# This mostly tests consistency. Tolerance chosen by experiment
# Do statistical tests on your own time.
np.random.seed(1)
neg_log_p = neg_log_normal(2, 0.1)
samples = hamiltonian_monte_carlo(100, neg_log_p, np.array(0.0))
assert samples.shape[0] == 100
assert_allclose(2.0, np.mean(samples), atol=0.02)
assert_allclose(0.1, np.std(samples), atol=0.007)
def test_hamiltonian_monte_carlo_mv():
np.random.seed(1)
mu = np.arange(2)
cov = 0.8 * np.ones((2, 2)) + 0.2 * np.eye(2)
neg_log_p = AutogradPotential(neg_log_mvnormal(mu, cov))
samples = hamiltonian_monte_carlo(100,
neg_log_p,
np.zeros(mu.shape),
path_len=2.0)
assert samples.shape[0] == 100
assert_allclose(mu, np.mean(samples, axis=0), atol=0.3)
assert_allclose(cov, np.cov(samples.T), atol=0.5)
def test_pymc3_interface():
np.random.seed(3)
with pm.Model() as model:
pm.Normal("x", mu=0.0, sigma=1.0, shape=10)
potential = PyMC3Potential()
initial_q = potential.bijection.map(model.test_point)
samples = hamiltonian_monte_carlo(500, potential, initial_q)
assert samples.shape[0] == 500
assert samples.shape[1] == 10
assert_allclose(0.0, np.mean(samples, axis=0), atol=0.13)
assert_allclose(1.0, np.var(samples, axis=0), atol=0.17)
"font.family": "serif",
"figure.facecolor": "#fffff8",
"axes.facecolor": "#fffff8",
"figure.constrained_layout.use": True,
"font.size": 14.0,
"hist.bins": "auto",
"lines.linewidth": 3.0,
"lines.markeredgewidth": 2.0,
"lines.markerfacecolor": "none",
"lines.markersize": 8.0,
}
)
### Example 1 ###
samples = hamiltonian_monte_carlo(
2000, AutogradPotential(neg_log_normal(0, 0.1)), initial_position=0.0
)
### Plot 1 ###
fig, ax = plt.subplots(figsize=FIGSIZE)
ax.hist(samples, bins="auto")
ax.axvline(0, color="C1", linestyle="--")
ax.set_title("1D Gaussians!")
plt.savefig(os.path.join(HERE, "plot1.png"))
### Example 2 ###
samples, positions, momentums, accepted, p_accepts = hmc_slow(
50, AutogradPotential(neg_log_normal(0, 0.1)), 0.0, step_size=0.01
)
### Plot 2 ###
