On the effect of HB covariance matrix prior settings: A simulation study

The authors conduct an extensive simulation study to substantially contribute to the question how HB prior parameter settings (i.e. the prior variance and the prior degrees of freedom) affect the performance of HB-CBC models. The statistical performance of HB is evaluated under experimentally varying conditions based on six experimental factors using criteria for goodness-of-fit, parameter recovery and predictive accuracy. The results indicate that the prior degrees of freedom play a negligible role as there is not any noticeable impact on the performance of HB when varying that factor. For increasing prior variance levels overfitting problems occur that markedly affect parameter recovery and model fit, and a number of related interaction effects with regard to the settings for the prior variance can be observed both at the upper and lower level of the HB model. Perhaps the most striking finding however is that the predictive performance of HB-CBC is hardly affected by an increase of the prior variance. Many of our findings regarding the parameter settings of the inverse Wishart prior contrast those reported in previously proposed empirical studies.