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 b...
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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), zeroinflated 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.
probabilistic programming languages are used to write probabilistic models to make probabilistic inferences. A number of rigorous semantics have been developed to reason about transformations of probabilistic programs...
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probabilistic programming languages are used to write probabilistic models to make probabilistic inferences. A number of rigorous semantics have been developed to reason about transformations of probabilistic programs and their execution. We propose to investigate the formalization of such a semantics to allow for the formal verification of probabilistic programs. Concretely, we extend an existing formalization of measure and integration theory in the Rocq prover, a proof assistant based on dependent type theory, with s-finite kernels, a mathematical structure to interpret typing judgments in the semantics of a probabilistic programming language. We explain the issues raised by organizing kernels as a hierarchy of mathematical structures and use the latter to formalize the semantics of a first-order probabilistic programming language. We use this semantics to establish generic properties of this language, prove rewriting laws to perform symbolic evaluation, and reason about iteration.
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