Radial basis functions for multivariable interpolation: a review
Algorithms for approximation
Bayesian radial basis functions of variable dimension
Neural Computation
Efficient sampling schemes for Bayesian MARS models with many predictors
Statistics and Computing
Signal Processing
A general approach to heteroscedastic linear regression
Statistics and Computing
Learning to Recognize Objects with Little Supervision
International Journal of Computer Vision
Predictive performance of Dirichlet process shrinkage methods in linear regression
Computational Statistics & Data Analysis
Bayesian skew selection for multivariate models
Computational Statistics & Data Analysis
Bayesian variable selection and model averaging in the arbitrage pricing theory model
Computational Statistics & Data Analysis
A sign based loss approach to model selection in nonparametric regression
Statistics and Computing
Bayesian Generalized Kernel Mixed Models
The Journal of Machine Learning Research
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This paper discusses a Bayesian approach to nonparametric regression initially proposed by Smith and Kohn (1996. Journal of Econometrics 75: 317–344). In this approach the regression function is represented as a linear combination of basis terms. The basis terms can be univariate or multivariate functions and can include polynomials, natural splines and radial basis functions. A Bayesian hierarchical model is used such that the coefficient of each basis term can be zero with positive prior probability. The presence of basis terms in the model is determined by latent indicator variables. The posterior mean is estimated by Markov chain Monte Carlo simulation because it is computationally intractable to compute the posterior mean analytically unless a small number of basis terms is used. The present article updates the work of Smith and Kohn (1996. Journal of Econometrics 75: 317–344) to take account of work by us and others over the last three years. A careful discussion is given to all aspects of the model specification, function estimation and the use of sampling schemes. In particular, new sampling schemes are introduced to carry out the variable selection methodology.