<Para ID="Par1">In this paper we consider the Bayesian approach to the problem of variable selection in normal linear regression models with related predictors. We adopt a generalized singular <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$g$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>g</mi> </math> </EquationSource> </InlineEquation>-prior distribution for the unknown model parameters and the beta-prime prior for the scaling factor <InlineEquation ID="IEq2"> <EquationSource...</equationsource></inlineequation></equationsource></equationsource></inlineequation></para>

We derive a class of matching priors for the shape parameter of the exponential power distribution, which controls the thickness of the density tails. It is shown that a second-order matching prior does not exist in the subclass of the considered priors.

HIV dynamic models, a set of ordinary differential equations (ODEs), have provided new understanding of the pathogenesis of HIV infection and the treatment effects of antiviral therapies. However, to estimate parameters for ODEs is very challenging due to the complexity of this nonlinear system....