Bayesian Analysis for Penalized Spline Regression Using WinBUGS

By Ciprian M. Crainiceanu, David Ruppert, Matt P. Wand. 2005

374 citations recorded by the source corpus.

Penalized splines can be viewed as BLUPs in a mixed model framework, which allows the use of mixed model software for smoothing. Thus, software originally developed for Bayesian analysis of mixed models can be used for penalized spline regression. Bayesian inference for nonparametric models enjoys the flexibility of nonparametric models and the exact inference provided by the Bayesian inferential machinery. This paper provides a simple, yet comprehensive, set of programs for the implementation of nonparametric Bayesian analysis in WinBUGS. Good mixing properties of the MCMC chains are obtained by using low-rank thin-plate splines, while simulation times per iteration are reduced employing WinBUGS specific computational tricks.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/45911f28ad0c5da26a3945071e11bfeb11d7bef9

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Citations in the corpus

Spatially Adaptive Bayesian Penalized Splines With Heteroscedastic Errors (2007, methodology): “Bayesian penalized splines (Ruppert, Wand, and Carroll 2003; Lang and Brezger 2004; Crainiceanu, Ruppert, and Wand 2005) use a stochastic process model as a prior for the regression function.”
Adaptive Bayesian Procedures Using Random Series Priors (2014, methodology): “Although a random series with a random number of terms has been used by practitioners in various applied models [Crainiceanu et al., 2005], theoretical properties of such priors have been studies only very recently for some particular choices of bases and prior distributions on the coefficients.”
Bivariate Binomial Spatial Modeling of Loa loa Prevalence in Tropical Africa (2008, background): “As discussed by Crainiceanu, Ruppert, and Wand (2005b), the prior distributions on the variance components should be treated carefully, because a poor choice of prior can seriously affect the smoothing function.”
WinBUGS for population ecologists: bayesian modeling using markov chain Monte Carlo methods (2009, methodology): “e . To implement the P-splines model in WinBUGS, it is convenient to express it as a Generalized Linear Mixed Model (GLMM), as shown by Crainiceanu et al. (2005) .”
BAYESIAN BETA REGRESSION: APPLICATIONS TO HOUSEHOLD EXPENDITURE DATA AND GENETIC DISTANCE BETWEEN FOOT‐AND‐MOUTH DISEASE VIRUSES (2007, methodology): “Using the connection between penalized splines and mixed models (Ruppert et al., 2003; Crainiceanu et al., 2005), we modelled b j ∼ N (0, τ ).”
ON SEMIPARAMETRIC REGRESSION WITH O'SULLIVAN PENALIZED SPLINES (2008, methodology): “Several examples of semiparametric regression with WinBUGS, including code, are given in Crainiceanu et al.(2005) and Zhao et al.(2006).”