Bayesian Analysis

Bayesian Nonparametric Tests via Sliced Inverse Modeling

Bo Jiang, Chao Ye, and Jun S. Liu

Full-text: Open access

Abstract

We study the problem of independence and conditional independence tests between categorical covariates and a continuous response variable, which has an immediate application in genetics. Instead of estimating the conditional distribution of the response given values of covariates, we model the conditional distribution of covariates given the discretized response (aka “slices”). By assigning a prior probability to each possible discretization scheme, we can compute efficiently a Bayes factor (BF)-statistic for the independence (or conditional independence) test using a dynamic programming algorithm. Asymptotic and finite-sample properties such as power and null distribution of the BF statistic are studied, and a stepwise variable selection method based on the BF statistic is further developed. We compare the BF statistic with some existing classical methods and demonstrate its statistical power through extensive simulation studies. We apply the proposed method to a mouse genetics data set aiming to detect quantitative trait loci (QTLs) and obtain promising results.

Article information

Source
Bayesian Anal. Volume 12, Number 1 (2017), 89-112.

Dates
First available in Project Euclid: 19 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.ba/1453211961

Digital Object Identifier
doi:10.1214/16-BA993

Mathematical Reviews number (MathSciNet)
MR3597568

Subjects
Primary: 62G10: Hypothesis testing
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures 62P10: Applications to biology and medical sciences

Keywords
Bayes factor dynamic programming non-parametric tests sliced inverse model variable selection

Citation

Jiang, Bo; Ye, Chao; Liu, Jun S. Bayesian Nonparametric Tests via Sliced Inverse Modeling. Bayesian Anal. 12 (2017), no. 1, 89--112. doi:10.1214/16-BA993. https://projecteuclid.org/euclid.ba/1453211961


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Supplemental materials

  • Supplement to “Bayesian Nonparametric Tests via Sliced Inverse Modeling”. We provide additional supporting materials that include detailed proofs and additional empirical results.