def test_log_beta_stirling(tol):
x = torch.logspace(-5, 5, 200)
y = x.unsqueeze(-1)
expected = log_beta(x, y)
actual = log_beta(x, y, tol=tol)
assert (actual <= expected).all()
assert (expected < actual + tol).all()
def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
n = self.total_count
k = value
a = self.concentration1
b = self.concentration0
tol = self.approx_log_prob_tol
return (log_binomial(n, k, tol) + log_beta(k + a, n - k + b, tol) -
log_beta(a, b, tol))
def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
post_value = self.concentration + value
return (-log_beta(self.concentration, value + 1) - post_value.log() +
self.concentration * self.rate.log() - post_value *
(1 + self.rate).log())