Bayesian Analysis

Learning Semiparametric Regression with Missing Covariates Using Gaussian Process Models

Abhishek Bishoyi, Xiaojing Wang, and Dipak K. Dey

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Abstract

Missing data often appear as a practical problem while applying classical models in the statistical analysis. In this paper, we consider a semiparametric regression model in the presence of missing covariates for nonparametric components under a Bayesian framework. As it is known that Gaussian processes are a popular tool in nonparametric regression because of their flexibility and the fact that much of the ensuing computation is parametric Gaussian computation. However, in the absence of covariates, the most frequently used covariance functions of a Gaussian process will not be well defined. We propose an imputation method to solve this issue and perform our analysis using Bayesian inference, where we specify the objective priors on the parameters of Gaussian process models. Several simulations are conducted to illustrate effectiveness of our proposed method and further, our method is exemplified via two real datasets, one through Langmuir equation, commonly used in pharmacokinetic models, and another through Auto-mpg data taken from the StatLib library.

Article information

Source
Bayesian Anal., Advance publication (2018), 25 pages.

Dates
First available in Project Euclid: 9 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.ba/1554775288

Digital Object Identifier
doi:10.1214/18-BA1136

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Gaussian processes missing at random missing covariates nonparametric regression semiparametric regression

Rights
Creative Commons Attribution 4.0 International License.

Citation

Bishoyi, Abhishek; Wang, Xiaojing; Dey, Dipak K. Learning Semiparametric Regression with Missing Covariates Using Gaussian Process Models. Bayesian Anal., advance publication, 9 April 2019. doi:10.1214/18-BA1136. https://projecteuclid.org/euclid.ba/1554775288


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Supplemental materials

  • Supplementary Materials for “Learning Semiparametric Regression with Missing Covariates Using Gaussian Process Models”. We have restated about the four conditions used in Ren et al. (2012) and the derivation for the Conditional Distribution of $\mathbf{x}^{mis}$ Given $\mathbf{x}^{obs}$ in Section S.1 and Section S.2 of the supplement, respectively. Moreover, we have put the detailed results of MSEx, PMSE and DIC for different covariance kernels in Simulation II of Section 4.2 as Section S.3 of the supplement material. Also, in Section S.4 and Section S.5 of the supplement material, we have included the MCMC sampling scheme for Langmuir model estimation as well as the MCMC sampling scheme for Log Model Estimation for Section 5.2. See more details in Supplement S (http://doi.org/10.2307/1390675).