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Scheipl, Fabian (2010): Normal-Mixture-of-Inverse-Gamma Priors for Bayesian Regularization and Model Selection in Structured Additive Regression Models. Department of Statistics: Technical Reports, No.84
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Abstract

In regression models with many potential predictors, choosing an appropriate subset of covariates and their interactions at the same time as determining whether linear or more flexible functional forms are required is a challenging and important task. We propose a spike-and-slab prior structure in order to include or exclude single coefficients as well as blocks of coefficients associated with factor variables, random effects or basis expansions of smooth functions. Structured additive models with this prior structure are estimated with Markov Chain Monte Carlo using a redundant multiplicative parameter expansion. We discuss shrinkage properties of the novel prior induced by the redundant parameterization, investigate its sensitivity to hyperparameter settings and compare performance of the proposed method in terms of model selection, sparsity recovery, and estimation error for Gaussian, binomial and Poisson responses on real and simulated data sets with that of component-wise boosting and other approaches.