Bayesian regression models for ecological count data in PyMC3

Abstract

Ecological inferences need structurally flexible statistical models to accommodate complex ecological phenomena. PyMC3 is a Probabilistic Programming Language (PPL) and allows for custom statistical distributions to build complex statistical models. This study used PyMC3 to implement Bayesian generalized Poisson (GP), zero-inflated GP, and hurdle GP regression models for over- and under-dispersed counts. The Bayesian GP regression models were fitted to simulated counts and real-world counts of over- and under-dispersion, respectively. Coefficient estimates of the Bayesian regression models were consistent with the known values used in the simulations and those of published work or models. Simulations demonstrated that Bayesian GP regression models with the NUTS sampler worked correctly for under-dispersed counts if the number of non-zero frequency classes was five or more. PyMC3 is not only flexible for building complex statistical models using custom likelihood functions, but also syntactically concise. The programming flexibility of PyMC3 can provide ecologists and environmental scientists with flexible, robust Bayesian computational platforms.