A comparative study on high-dimensional bayesian regression with binary predictors

Bayesian regression models have been widely studied and adopted in the statistical literature. Many studies consider the development of reliable priors to select the relevant variables and derive accurate posterior predictive distributions. Moreover in the context of small high-dimensional data, where the number of observations is very small with respect to the number of predictors, sparsity is assumed and many parameters can be set to values close to zero without affecting the fit of the model. Aim of this work is to develop a comparative analysis to empirically evaluate the performances of several Bayesian regression approaches in these contexts. In this study we assume that the predictors can be expressed only as binary variables coding the presence or the absence of a particular characteristic of the system. This binary structure is often present in many real studies, in particular in laboratory experimentation and in very high-dimension genome wide association studies.