def test_sample(concentration, rate, n_samples=int(1e6)):
samples = InverseGamma(concentration, rate).sample((n_samples, ))
mean, std = samples.mean().item(), samples.std().item()
expected_mean = rate / (concentration - 1.0)
expected_std = rate / (
(concentration - 1.0) * math.sqrt(concentration - 2.0))
assert_equal(mean, expected_mean, prec=1e-2)
assert_equal(std, expected_std, prec=0.03)
def mixed_simulator(theta):
# Extract parameters
beta, ps = theta[:, :1], theta[:, 1:]
# Sample choices and rts independently.
choices = Binomial(probs=ps).sample()
rts = InverseGamma(concentration=2 * torch.ones_like(beta),
rate=beta).sample()
return torch.cat((rts, choices), dim=1)
def marginal(self, xts):
sup = xts[1::] - self.phi * xts[0:-1]
sup = np.power(sup, 2)
sup = 0.5 * np.sum(sup)
bup = np.exp(-xts[1::])
bup = bup * (np.power(self.yts, 2))
bup = 0.5 * np.sum(bup)
T = xts.shape[0] - 1
a = self.a + 0.5 * T
b_sigma2 = self.b + sup
b_beta2 = self.b + bup
ig_sigma2 = IG(a, b_sigma2)
ig_beta2 = IG(a, b_beta2)
sigma2 = ig_sigma2.sample().numpy()
beta2 = ig_beta2.sample().numpy()
return (sigma2, beta2)
def iid_likelihood(self, theta: torch.Tensor) -> torch.Tensor:
"""Returns the likelihood summed over a batch of i.i.d. data."""
lp_choices = torch.stack(
[
Binomial(probs=th.reshape(1, -1)).log_prob(self.x_o[:, 1:])
for th in theta[:, 1:]
],
dim=1,
)
lp_rts = torch.stack(
[
InverseGamma(concentration=2 * torch.ones_like(beta_i),
rate=beta_i).log_prob(self.x_o[:, :1])
for beta_i in theta[:, :1]
],
dim=1,
)
joint_likelihood = (lp_choices + lp_rts).reshape(
self.x_o.shape[0], theta.shape[0])
return joint_likelihood.sum(0)
def test_log_prob(concentration, rate, value):
value = torch.tensor(value)
log_prob = InverseGamma(concentration, rate).log_prob(value)
expected_log_prob = (Gamma(concentration, rate).log_prob(1.0 / value) -
2.0 * value.log())
assert_equal(log_prob, expected_log_prob, prec=1e-6)