Bayesian Regularization and Model Choice in Structured Additive Regression

In regression models with a large number of potential model terms, the selection of an appropriate subset of covariates and their interactions is an important challenge for data analysis, as is the choice of the appropriate representation of their impact on the quantities to be estimated such as deciding between linear or smooth non-linear effects. The main part of this work is dedicated to the development, implementation and validation of an extension of stochastic search variable selection (SSVS) for structured additive regression models aimed at finding and estimating appropriate and parsimonious model representations. The approach described here is the first implementation of fully Bayesian variable selection and model choice for general responses from the exponential family in generalized additive mixed models (GAMM) available in free and open source software. It is based on a spike-and-slab prior on the regression coefficients with an inno-vative multiplicative parameter expansion that induces desirable shrinkag