PEPBVS - Bayesian Variable Selection using Power-Expected-Posterior Prior

Performs Bayesian variable selection under normal linear models for the data with the model parameters following as prior distributions either the power-expected-posterior (PEP) or the intrinsic (a special case of the former) (Fouskakis and Ntzoufras (2022) <doi: 10.1214/21-BA1288>, Fouskakis and Ntzoufras (2020) <doi: 10.3390/econometrics8020017>). The prior distribution on model space is the uniform over all models or the uniform on model dimension (a special case of the beta-binomial prior). The selection is performed by either implementing a full enumeration and evaluation of all possible models or using the Markov Chain Monte Carlo Model Composition (MC3) algorithm (Madigan and York (1995) <doi: 10.2307/1403615>). Complementary functions for hypothesis testing, estimation and predictions under Bayesian model averaging, as well as, plotting and printing the results are also provided. The results can be compared to the ones obtained under other well-known priors on model parameters and model spaces.