Investigate suspicious implementation of Poisson.logpdf

[fsaad]

Specifically the following lines

cgpm/src/primitives/poisson.py

Lines 146 to 170 in 46e1d8d

	@staticmethod
	def calc_predictive_logp(x, N, sum_x, a, b):
	an, bn = Poisson.posterior_hypers(N, sum_x, a, b)
	am, bm = Poisson.posterior_hypers(N+1, sum_x+x, a, b)
	ZN = Poisson.calc_log_Z(an, bn)
	ZM = Poisson.calc_log_Z(am, bm)
	return ZM - ZN - gammaln(x+1)
	@staticmethod
	def calc_logpdf_marginal(N, sum_x, sum_log_fact_x, a, b):
	an, bn = Poisson.posterior_hypers(N, sum_x, a, b)
	Z0 = Poisson.calc_log_Z(a, b)
	ZN = Poisson.calc_log_Z(an, bn)
	return ZN - Z0 - sum_log_fact_x
	@staticmethod
	def posterior_hypers(N, sum_x, a, b):
	an = a + sum_x
	bn = b + N
	return an, bn
	@staticmethod
	def calc_log_Z(a, b):
	Z = gammaln(a) - a*log(b)
	return Z

The posterior predictive distribution should be a negative binomial with n = a' and p = 1 / (1 + b'), or possibly p = 1 - 1/(1+b'), depending on the parameterization. From a cursory test the values returned by Poisson.calc_predictive_logp do not correspond to the negative binomial probabilities from scipy.stats.nbinom.