# A novel algorithmic approach to Bayesian Logic Regression

## TL;DR

This paper introduces GMJMCMC, an advanced evolutionary algorithm for Bayesian logic regression, capable of identifying complex multi-way genetic interactions with high power, demonstrated through simulations and real genetic data analysis.

## Contribution

It adapts GMJMCMC for Bayesian model selection in logic regression, enabling detection of higher-order interactions previously difficult to identify.

## Key findings

- GMJMCMC effectively detects three- and four-way interactions.
- The method shows high power in simulation studies.
- Applied to genetic data, it uncovers significant epistatic effects.

## Abstract

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 mapping data for Recombinant Inbred Lines in \textit{Arabidopsis thaliana} and from a backcross population in \textit{Drosophila} where we identify several interesting epistatic effects. The method is implemented in an R package which is available on github.