Bayes Estimate and Inference for Entropy and Information Index of Fit
定义了量化熵，利用狄利克雷过程先验和最大熵候选模型，给出了熵和Kullback-Leibler信息指数的贝叶斯估计与推断，并证明了估计的一致性。
This article defines a quantized entropy and develops Bayes estimates and inference for the entropy and a Kullback–Leibler information index of the model fit. We use a Dirichlet process prior for the unknown data-generating distribution with a maximum entropy candidate model as the expected distribution. This formulation produces prior and posterior distributions for the quantized entropy, the information index of fit, the moments, and the model parameters. The posterior mean of the quantized entropy provides a Bayes estimate of entropy under quadratic loss. The consistency of the Bayes estimates and the information index are shown. The implementation and the performances of the Bayes estimates are illustrated using data simulated from exponential, gamma, and lognormal distributions.