Applied Bayesian Modelling, 2nd Edition

3.5.1 The -prior approach

Results of regression model selection depend on the priors adopted for regression coefficients, with diffuse (non-informative) priors generally not recommended. Information on the predictors (though not responses) is made use of under the -prior approach, originally proposed for linear regression with a metric outcome , usually assuming normal errors, and known predictors (Fernandez et al., 2001; Liang et al., 2008). With denoting the predictor matrix under model (defined by retaining the subset of predictors with , the g-prior specifies

where is the residual precision, ...