def binom(n, k):
"""
binom(n, k)
Binomial coefficient
"""
return exp(gammaln(1 + n) - gammaln(1 + k) - gammaln(1 + n - k))
def eval_sh_jacobi(n, p, q, x, out=None):
"""
eval_sh_jacobi(n, p, q, x, out=None)
Evaluate shifted Jacobi polynomial at a point.
"""
factor = exp(gammaln(1 + n) + gammaln(n + p) - gammaln(2 * n + p))
return factor * eval_jacobi(n, p - q, q - 1, 2 * x - 1)
def ln_prob(self, val):
"""Returns the log prior probability of val.
Parameters
----------
val: Union[float, int, array_like]
Returns
-------
Union[float, array_like]: Prior probability of val
"""
return gammaln(0.5 * (self.df + 1)) - gammaln(0.5 * self.df)\
- np.log(np.sqrt(np.pi * self.df) * self.scale) - (self.df + 1) / 2 *\
np.log(1 + ((val - self.mu) / self.scale) ** 2 / self.df)
def ln_prob(self, val):
"""Returns the log prior probability of val.
Parameters
----------
val: Union[float, int, array_like]
Returns
-------
Union[float, array_like]: Prior probability of val
"""
if isinstance(val, (float, int)):
if val < self.minimum:
_ln_prob = -np.inf
else:
_ln_prob = xlogy(self.k - 1, val) - val / self.theta - xlogy(
self.k, self.theta) - gammaln(self.k)
else:
_ln_prob = -np.inf * np.ones(len(val))
idx = (val >= self.minimum)
_ln_prob[idx] = xlogy(self.k - 1, val[idx]) - val[idx] / self.theta\
- xlogy(self.k, self.theta) - gammaln(self.k)
return _ln_prob
def ll_F_Y(self, F, Y):
_log_lambda = (F + self.offset)
return (Y * _log_lambda - np.exp(_log_lambda) - gammaln(Y + 1))[:, :, 0], (Y - np.exp(F + self.offset))[:, :, 0]
def ll_F_Y(self, F, Y):
_log_lambda = F + self.offset
return (Y * _log_lambda - np.exp(_log_lambda) - gammaln(Y + 1))[:, :, 0], (Y - np.exp(F + self.offset))[:, :, 0]