Bayesian generalized additive model selection

Generalized additive models (GAMs) offer a parsimonious, flexible and interpretable framework for regression, particularly when handling a large numbers of candidate predictors. This thesis addresses the GAM variable selection problem: categorizing each candidate predictor's effect type to be linear, non-linear or zero on the mean response. We use Bayesian model selection paradigms and group least absolute shrinkage and selection operator (LASSO) priors. Two types of priors are explored for the sparse fits. The first, Laplace-Zero and Grouped Lasso-Zero priors, is applied to Gaussian and binary responses. The second, (Grouped) Horseshoe priors, is used for Gaussian and count responses. For both prior types, tailored auxiliary variable representations enable the Markov chain Monte Carlo (MCMC) sampling reduce to the Gibbs sampling or to slice sampling. To improve computational scalability and speed, we also derive the mean field variational Bayes (MFVB) algorithms under the Laplace-Zero and Grouped Lasso-Zero priors. The GAM selection framework is further extended to generalized additive mixed model (GAMM) with random intercept. Finally, the properties of the Grouped Horseshoe distribution and its use in Bayesian GAM selection are investigated. While many characteristics of univariate Horseshoe distribution are carried over, some distinctions arise in the grouped case.

Author dc:creator

• He, Virginia Xiaojun

Statement dc:rights

• info:eu-repo/semantics/openAccess
• The author owns the copyright in this thesis including all reproduction and reuse rights for the work. The work may not be altered without the permission of the copyright owner. Attribution is essential when quoting or paraphrasing from this thesis.
• © 2025 Virginia Xiaojun He
• au.edu.uts.lib/cph

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10453/191847

OAI identifier oai:identifier

oai:opus.lib.uts.edu.au:10453/191847