Information Measures and Bayesian Hierarchical Models
研究了贝叶斯分层模型中先验分布的超参数层级越高、信息量越少的性质，基于f散度统一了相关定理并扩展了适用信息度量。
Abstract We consider the Bayesian statistical models in which the prior distribution of the parameter vector θ1 in the distribution of an observable random vector X is to be specified in a hierarchical fashion and one wants to learn about the hyperparameters at each level of this prior distribution. It is shown that for a wide class of information measures, based on the so-called f divergence, the information decreases as one moves to higher levels of hyperparameters. This result unifies all the theorems in Goel and DeGroot (1981) and provides several other information measures for which the above desirable property holds. Key Words: Hyperparameters f divergenceAmount of sample information