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.Comment: 32 pages, 7 figure