High-dimensional Bayesian inference in nonparametric additive models

Zuofeng Shang, Ping Li

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive compo- nents may be larger than the sample size, though ideally the true model is believed to include only a small number of components. Bayesian approaches can conduct stochastic model search and fulfill flexible parameter estimation by stochastic draws. The theory shows that the proposed model selection method has satisfactory properties. For instance, when the hyper-parameter associated with the model prior is correctly specified, the true model has posterior probability approaching one as the sample size goes to infinity; when this hyperparameter is incorrectly specified, the selected model is still acceptable since asymptotically it is shown to be nested in the true model. To enhance model flexibility, two new g-priors are proposed and their theoretical performance is investigated. We also propose an efficient reversible jump MCMC algorithm to handle the computational issues. Several simulation examples are provided to demonstrate the advantages of our method.

Original languageEnglish (US)
Pages (from-to)2804-2847
Number of pages44
JournalElectronic Journal of Statistics
Volume8
DOIs
StatePublished - 2014

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Bayesian group selection
  • Generalized hyper-g prior
  • Generalized zellner-siow prior
  • Nonparametric additive model
  • Posterior model consistency
  • Reversible jump MCMC
  • Size-control prior
  • Ultrahigh-dimensionality

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