文章基本信息

标题：A variational Bayes approach to a semiparametric regression using Gaussian process priors
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作者：Victor M. H. Ong ; David K. Mensah ; David J. Nott 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2017
卷号：11
期号：2
页码：4258-4296
DOI：10.1214/17-EJS1324
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.