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Logic regression was developed more than a decade ago as a tool to constructpredictors from Boolean combinations of binary covariates. It has been mainlyused to model epistatic effects in genetic association studies, which is veryappealing due to the intuitive interpretation of logic expressions to describethe interaction between genetic variations. Nevertheless logic regression has(partly due to computational challenges) remained less well known than otherapproaches to epistatic association mapping. Here we will adapt an advancedevolutionary algorithm called GMJMCMC (Genetically modified Mode Jumping MarkovChain Monte Carlo) to perform Bayesian model selection in the space of logicregression models. After describing the algorithmic details of GMJMCMC weperform a comprehensive simulation study that illustrates its performance givenlogic regression terms of various complexity. Specifically GMJMCMC is shown tobe able to identify three-way and even four-way interactions with relativelylarge power, a level of complexity which has not been achieved by previousimplementations of logic regression. We apply GMJMCMC to reanalyze QTL mappingdata for Recombinant Inbred Lines in \textit{Arabidopsis thaliana} and from abackcross population in \textit{Drosophila} where we identify severalinteresting epistatic effects. The method is implemented in an R package whichis available on github.

A novel algorithmic approach to Bayesian Logic Regression