We use Bayesian model selection paradigms, such as group least absolute shrinkage and selection operator priors, to facilitate generalized additive model selection. Our approach allows for the effects of continuous predictors to be categorized as either zero, linear or non-linear. Employment of carefully tailored auxiliary variables results in Gibbsian Markov chain Monte Carlo schemes for practical implementation of the approach. In addition, mean field variational algorithms with closed form updates are obtained. Whilst not as accurate, this fast variational option enhances scalability to very large data sets. A package in the R language aids use in practice.

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