We consider the fitting of a Bayesian model to grouped data in which observations are assumed normally distributed around group means that are themselves normally distributed, and consider several alternatives for accommodating the possibility of heteroscedasticity within the data. We consider the case where the underlying distribution of the variances is unknown, and investigate several candidate prior distributions for those variances. In each case, the parameters of the candidate priors (the hyperparameters) are themselves given uninformative priors (hyperpriors). The most mathematically convenient model for the group variances is to assign them inverse gamma distributed priors, the inverse gamma distribution being the conjugate prior distribution for the unknown variance of a normal population. We demonstrate that for a wide class of underlying distributions of the group variances, a model that assigns the variances an inverse gamma-distributed prior displays favorable goodness-of-fit properties relat...
['Alan Herschtal', 'Farshad Foroudi', 'Tomas Kron', 'Kerrie Mengersen']
A Comparison of Bayesian Models of Heteroscedasticity in Nested Normal Data