Nonparametric Goodness of Fit via Cross-Validation Bayes Factors | Zendy

Jeffrey D. Hart | Zendy; Taeryon Choi | Zendy

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Nonparametric Goodness of Fit via Cross-Validation Bayes Factors

Author(s) -

Jeffrey D. Hart,

Taeryon Choi

Publication year - 2016

Publication title -

bayesian analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.685

H-Index - 58

eISSN - 1936-0975

pISSN - 1931-6690

DOI - 10.1214/16-ba1018

Subject(s) - kernel (algebra) , nonparametric statistics , kernel density estimation , goodness of fit , variable kernel density estimation , bayes factor , parametric statistics , mathematics , bayes' theorem , cross validation , statistics , computer science , marginal likelihood , bayesian probability , kernel method , artificial intelligence , support vector machine , combinatorics , estimator

A nonparametric Bayes procedure is proposed for testing the t of a parametric model for a distribution. Alternatives to the parametric model are kernel density estimates. Data splitting makes it possible to use kernel estimates for this purpose in a Bayesian setting. A kernel estimate indexed by bandwidth is computed from one part of the data, a training set, and then used as a model for the rest of the data, a validation set. A Bayes factor is calculated from the validation set by comparing the marginal for the kernel model with the marginal for the parametric model of interest. A simulation study is used to investigate how large the training set should be, and examples involving astronomy and wind data are provided. A proof of Bayes consistency of the proposed test is also given.

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