from jax import lax, random
import jax.numpy as np
from jax.scipy.special import gammaln
from numpyro.distributions import constraints
from numpyro.distributions.continuous import Beta, Gamma
from numpyro.distributions.discrete import Binomial, Poisson
from numpyro.distributions.distribution import Distribution
from numpyro.distributions.util import promote_shapes, validate_sample
def _log_beta(x, y):
return gammaln(x) + gammaln(y) - gammaln(x + y)
[docs]class BetaBinomial(Distribution):
r"""
Compound distribution comprising of a beta-binomial pair. The probability of
success (``probs`` for the :class:`~numpyro.distributions.Binomial` distribution)
is unknown and randomly drawn from a :class:`~numpyro.distributions.Beta` distribution
prior to a certain number of Bernoulli trials given by ``total_count``.
:param numpy.ndarray concentration1: 1st concentration parameter (alpha) for the
Beta distribution.
:param numpy.ndarray concentration0: 2nd concentration parameter (beta) for the
Beta distribution.
:param numpy.ndarray total_count: number of Bernoulli trials.
"""
arg_constraints = {'concentration1': constraints.positive, 'concentration0': constraints.positive,
'total_count': constraints.nonnegative_integer}
def __init__(self, concentration1, concentration0, total_count=1, validate_args=None):
batch_shape = lax.broadcast_shapes(np.shape(concentration1), np.shape(concentration0),
np.shape(total_count))
self.concentration1 = np.broadcast_to(concentration1, batch_shape)
self.concentration0 = np.broadcast_to(concentration0, batch_shape)
self.total_count, = promote_shapes(total_count, shape=batch_shape)
self._beta = Beta(self.concentration1, self.concentration0)
super(BetaBinomial, self).__init__(batch_shape, validate_args=validate_args)
[docs] def sample(self, key, sample_shape=()):
key_beta, key_binom = random.split(key)
probs = self._beta.sample(key_beta, sample_shape)
return Binomial(self.total_count, probs).sample(key_binom)
@validate_sample
def log_prob(self, value):
log_factorial_n = gammaln(self.total_count + 1)
log_factorial_k = gammaln(value + 1)
log_factorial_nmk = gammaln(self.total_count - value + 1)
return (log_factorial_n - log_factorial_k - log_factorial_nmk +
_log_beta(value + self.concentration1, self.total_count - value + self.concentration0) -
_log_beta(self.concentration0, self.concentration1))
@property
def mean(self):
return self._beta.mean * self.total_count
@property
def variance(self):
return self._beta.variance * self.total_count * (self.concentration0 + self.concentration1 + self.total_count)
@property
def support(self):
return constraints.integer_interval(0, self.total_count)
[docs]class GammaPoisson(Distribution):
r"""
Compound distribution comprising of a gamma-poisson pair, also referred to as
a gamma-poisson mixture. The ``rate`` parameter for the
:class:`~numpyro.distributions.Poisson` distribution is unknown and randomly
drawn from a :class:`~numpyro.distributions.Gamma` distribution.
:param numpy.ndarray concentration: shape parameter (alpha) of the Gamma distribution.
:param numpy.ndarray rate: rate parameter (beta) for the Gamma distribution.
"""
arg_constraints = {'concentration': constraints.positive, 'rate': constraints.positive}
support = constraints.nonnegative_integer
def __init__(self, concentration, rate=1., validate_args=None):
self._gamma = Gamma(concentration, rate)
self.concentration = self._gamma.concentration
self.rate = self._gamma.rate
super(GammaPoisson, self).__init__(self._gamma.batch_shape, validate_args=validate_args)
[docs] def sample(self, key, sample_shape=()):
key_gamma, key_poisson = random.split(key)
rate = self._gamma.sample(key_gamma, sample_shape)
return Poisson(rate).sample(key_poisson)
@validate_sample
def log_prob(self, value):
post_value = self.concentration + value
return -_log_beta(self.concentration, value + 1) - np.log(post_value) + \
self.concentration * np.log(self.rate) - post_value * np.log1p(self.rate)
@property
def mean(self):
return self.concentration / self.rate
@property
def variance(self):
return self.concentration / np.square(self.rate) * (1 + self.rate)