def logp(value, n, p):
return bound(
factln(n) - factln(value).sum() + (value * at.log(p)).sum(),
value >= 0,
0 <= p,
p <= 1,
at.isclose(p.sum(), 1),
broadcast_conditions=False,
)
def logp(self, value):
n = self.n
p = self.p
return bound(
factln(n) - factln(value).sum() + (value * at.log(p)).sum(),
at.all(value >= 0),
at.all(0 <= p),
at.all(p <= 1),
at.isclose(p.sum(), 1),
broadcast_conditions=False,
)
def logp(self, x):
n = self.n
p = self.p
return bound(tt.sum(factln(n)) - tt.sum(factln(x)) +
tt.sum(x * tt.log(p)),
tt.all(x >= 0),
tt.all(tt.eq(tt.sum(x, axis=-1, keepdims=True), n)),
tt.all(p <= 1),
tt.all(tt.eq(tt.sum(p, axis=-1), 1)),
tt.all(tt.ge(n, 0)),
broadcast_conditions=False)
def logp(self, value):
n = self.n
p = self.p
return bound(
factln(n) - factln(value).sum() + (value * aet.log(p)).sum(),
value >= 0,
0 <= p,
p <= 1,
aet.isclose(p.sum(), 1),
broadcast_conditions=False,
)
def logp(self, value):
value_x = value[0][0]
value_y = value[0][1]
mu_x = self.mu_x
mu_y = self.mu_y
log_prob_x = bound(
logpow(mu_x, value_x) - factln(value_x) - mu_x,
mu_x >= 0, value_x >= 0)
log_prob_y = bound(
logpow(mu_y, value_y) - factln(value_y) - mu_y,
mu_y >= 0, value_y >= 0)
out = T.switch(1 * T.eq(mu_x, 0) * T.eq(value_x, 0), 0, log_prob_x)
out += T.switch(1 * T.eq(mu_x, 0) * T.eq(value_x, 0), 0, log_prob_y)
return out
def logp(self, value):
mu = self.mu
# mu^k
# PDF = ------------
# k! (e^mu - 1)
# log(PDF) = log(mu^k) - (log(k!) + log(e^mu - 1))
#
# See https://en.wikipedia.org/wiki/Zero-truncated_Poisson_distribution
p = logpow(mu,
value) - (factln(value) + pm.math.log(pm.math.exp(mu) - 1))
log_prob = bound(p, mu >= 0, value >= 0)
# Return zero when mu and value are both zero
return tt.switch(1 * tt.eq(mu, 0) * tt.eq(value, 0), 0, log_prob)
def logp_Poisson(self, value):
r"""
Calculate log-probability of Poisson distribution at specified value.
Switches to Gamma distribution when mu gets large (> 1000)
Parameters
----------
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple
values are desired the values must be provided in a numpy array or theano tensor
Returns
-------
TensorVariable
"""
# Return zero when mu and value are both zero, return Gamma log-probability when mu is > 1000,
# otherwise return Poisson log-probability
return tt.switch(
tt.gt(self.mu_biol, 1e3),
pm.Gamma.dist(mu=self.mu_biol,
sd=tt.sqrt(self.mu_biol)).logp(value),
tt.switch(
tt.eq(self.mu_biol, 0) * tt.eq(value, 0), 0,
bound(
logpow(self.mu_biol, value) - factln(value) - self.mu_biol,
self.mu_biol >= 0, value >= 0)))