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March 2020 A Novel Algorithmic Approach to Bayesian Logic Regression (with Discussion)
Aliaksandr Hubin, Geir Storvik, Florian Frommlet
Bayesian Anal. 15(1): 263-333 (March 2020). DOI: 10.1214/18-BA1141


Logic regression was developed more than a decade ago as a tool to construct predictors from Boolean combinations of binary covariates. It has been mainly used to model epistatic effects in genetic association studies, which is very appealing due to the intuitive interpretation of logic expressions to describe the interaction between genetic variations. Nevertheless logic regression has (partly due to computational challenges) remained less well known than other approaches to epistatic association mapping. Here we will adapt an advanced evolutionary algorithm called GMJMCMC (Genetically modified Mode Jumping Markov Chain Monte Carlo) to perform Bayesian model selection in the space of logic regression models. After describing the algorithmic details of GMJMCMC we perform a comprehensive simulation study that illustrates its performance given logic regression terms of various complexity. Specifically GMJMCMC is shown to be able to identify three-way and even four-way interactions with relatively large power, a level of complexity which has not been achieved by previous implementations of logic regression. We apply GMJMCMC to reanalyze QTL (quantitative trait locus) mapping data for Recombinant Inbred Lines in Arabidopsis thaliana and from a backcross population in Drosophila where we identify several interesting epistatic effects. The method is implemented in an R package which is available on github.


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Aliaksandr Hubin. Geir Storvik. Florian Frommlet. "A Novel Algorithmic Approach to Bayesian Logic Regression (with Discussion)." Bayesian Anal. 15 (1) 263 - 333, March 2020.


Published: March 2020
First available in Project Euclid: 20 December 2018

MathSciNet: MR4077212
Digital Object Identifier: 10.1214/18-BA1141

Keywords: Bayesian model averaging , Genetic algorithm , logic regression , mode jumping Monte Carlo Markov Chain , QTL mapping


Vol.15 • No. 1 • March 2020
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