Bayesian views of generalized additive modelling

Abstract: Generalized additive models (GAMs) are a commonly used, flexible framework applied to many problems in statistical ecology. GAMs are often considered to be a purely frequentist framework (`generalized linear models with wiggly bits'), however links between frequentist and Bayesian approaches to these models were highlighted early on in the literature. Bayesian thinking underlies many parts of the implementation in the popular R package \texttt{mgcv} as well as in GAM theory more generally. This article aims to highlight useful links (and differences) between Bayesian and frequentist approaches to smoothing, and their practical applications in ecology (with an \texttt{mgcv}-centric viewpoint). Here I give some background for these results then move onto two important topics for quantitative ecologists: term/model selection and uncertainty estimation.