Bayes Extended Estimators for Curved Exponential Families

The Bayesian predictive density has complex representation and does not belong to any finite-dimensional statistical model except for in limited situations. In this paper, we introduce its simple approximate employing projection onto a exponential family. Its theoretical properties are established parallelly those of the when belongs curved families. It is also demonstrated that asymptotically coincides with plugin posterior mean expectation parameter family, which refer as Bayes extended estimator. Information-geometric correspondence indicates can be represented infinite-dimensional Kullback–Leibler risk performance approximation by numerical simulations it approaches dimension family increases. suggests an reasonable size practically advantageous respect computational cost.