ABSTRACT
Bayesian statistical models provide a useful way to obtain inference and predictions for unobserved quantities in nature based on a solid foundation of mathematical rules pertaining to probability. Bayesian models are inherently parametric because they involve components that are specified as known probability distributions, the parameters of which are often of primary interest. Bayesian models rely on probability distributions and the concept of random variables. Stochastic Bayesian algorithms also rely on properties of random variables. The most useful way to characterize probability distributions in Bayesian models is with probability density functions; or probability mass functions for discrete random variables. Ecologists and environmental scientists have welcomed Bayesian hierarchical modeling in part because it meshes with how they think about the data-generating mechanisms and many complicated hierarchical models are easier to implement from a Bayesian perspective. A Bayesian statistical model is a formal mathematical description of stochastic data-generating mechanisms.
