## Electronic Journal of Statistics

### A variational Bayes approach to a semiparametric regression using Gaussian process priors

#### Abstract

This paper presents a variational Bayes approach to a semiparametric regression model that consists of parametric and nonparametric components. The assumed univariate nonparametric component is represented with a cosine series based on a spectral analysis of Gaussian process priors. Here, we develop fast variational methods for fitting the semiparametric regression model that reduce the computation time by an order of magnitude over Markov chain Monte Carlo methods. Further, we explore the possible use of the variational lower bound and variational information criteria for model choice of a parametric regression model against a semiparametric alternative. In addition, variational methods are developed for estimating univariate shape-restricted regression functions that are monotonic, monotonic convex or monotonic concave. Since these variational methods are approximate, we explore some of the trade-offs involved in using them in terms of speed, accuracy and automation of the implementation in comparison with Markov chain Monte Carlo methods and discuss their potential and limitations.

#### Article information

Source
Electron. J. Statist., Volume 11, Number 2 (2017), 4258-4296.

Dates
First available in Project Euclid: 8 November 2017

https://projecteuclid.org/euclid.ejs/1510111112

Digital Object Identifier
doi:10.1214/17-EJS1324

Mathematical Reviews number (MathSciNet)
MR3720915

Zentralblatt MATH identifier
06805092

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62F15: Bayesian inference

#### Citation

Ong, Victor M. H.; Mensah, David K.; Nott, David J.; Jo, Seongil; Park, Beomjo; Choi, Taeryon. A variational Bayes approach to a semiparametric regression using Gaussian process priors. Electron. J. Statist. 11 (2017), no. 2, 4258--4296. doi:10.1214/17-EJS1324. https://projecteuclid.org/euclid.ejs/1510111112

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