Bayesian Inference for the Negative Binomial Distribution via Polynomial Expansions

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Marketing Analytics for Data-Rich Environments (2016, unknown): “Bradlow, Hardie, and Fader (2002) and Everson and Bradlow (2002) derive closed-form Bayesian inference for models with nonconjugate priors and likelihood, such as the negative binomial and beta-binomial models, using series expansions.”
Count Models Based on Weibull Interarrival Times (2008, background): “Other models for occurrence dependence have been developed by Mullahy (1986), and Gourieroux and Visser (1997). One can also make the assumption that successive events are independent but the process intensity varies as a function of time.”
Bayesian mixed-effects inference on classification performance in hierarchical data sets (2012, background): “, integrable and normalized) variant, p(α,β) = 3 4 (α+β+1)−5/2 (7) which represents a special case of the generalization of (6) proposed by Everson and Bradlow (2002). This prior can be rewritten in an unnormalized, reparameterized form as p̃ (”
Moderated statistical tests for assessing differences in tag abundance (2007, background): “Bradlow et al. (2002) suggest a polynomial approximation in order to avoid the computation overheard of stochastic Markov Chain inference methods.”