The maximal dominated subsets of a statistical experiment (Q1273024)

A Bayesian experiment consisting of the prior \(\mu\) and the conditional distribution \(P^a\) is called dominated if the corresponding joint distribution is absolutely continuous with respect to the product of the marginal distributions. The author asks for conditions on \(\mu\) which guarantee this property. For this aim \(\mu\) is related to the system \({\mathcal A}^*\) of maximal sets of the parameter space \((A,{\mathcal A})\) defined by \({\mathcal A}^*= \{E \in {\mathcal A},\exists Q_E:P^a\ll Q_E,\;\forall a\in E\}\). Of special importance is whether \(\mu\) is atomic or diffuse.