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Applied Bayesian Modelling, 2nd Edition by Peter Congdon

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3.5.1 The c03-math-0548-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 c03-math-0549-prior approach, originally proposed for linear regression with a metric outcome c03-math-0550, usually assuming normal errors, and known predictors (Fernandez et al., 2001; Liang et al., 2008). With c03-math-0551 denoting the c03-math-0552 predictor matrix under model c03-math-0553 (defined by retaining the subset of c03-math-0554 predictors with c03-math-0555, the g-priorc03-math-0556 specifies

where is the residual precision, ...

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