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Bayesian Identification, Selection And Estimation Of Functions In High-Dimensional Additive Models, Anastasios Panagiotelis, Michael Smith

Michael Stanley Smith

In this paper we propose an approach to both estimate and select unknown smooth functions in an additive model with potentially many functions. Each function is written as a linear combination of basis terms, with coefficients regularized by a proper linearly constrained Gaussian prior. Given any potentially rank deficient prior precision matrix, we show how to derive linear constraints so that the corresponding effect is identified in the additive model. This allows for the use of a wide range of bases and precision matrices in priors for regularization. By introducing indicator variables, each constrained Gaussian prior is augmented with a …