Rejoinder for the discussion of the paper "A novel algorithmic approach to Bayesian Logic Regression"

We would like to begin this rejoinder with expressing our sincere gratitude to all of the discussants for their interesting and thought-provoking comments and remarks. We also feel heartily thankful to the editorial board of Bayesian Analysis for giving us the opportunity to publish our paper entitled "A novel algorithmic approach to Bayesian logic regression" (Hubin et al., 2020a) as a discussion article. Logic regression is a tool to model nonlinear relationships between binary covariates and some response variable by constructing predictors as Boolean combinations. The number of possible logic expressions grows exponentially with the number of binary variables involved, making the model search significantly harder with the increasing complexity of Boolean combinations. Due to Boolean equivalence, it is in fact almost impossible to specify the full model space a priori even for a relatively small number of covariates.