Bayesian nonparametric tests via sliced inverse modeling

TL;DR

This paper introduces a Bayesian nonparametric approach for independence and conditional independence testing between categorical covariates and continuous responses, using sliced inverse modeling and dynamic programming for efficient computation.

Contribution

It proposes a novel Bayesian method that models covariates given discretized responses, enabling efficient independence testing with theoretical and empirical validation.

Findings

The BF statistic shows strong power in simulations.

The method effectively detects QTLs in genetics data.

It outperforms some classical independence tests.

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.