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- Title
Parametric Bayesian Estimation of Differential Entropy and Relative Entropy.
- Authors
Gupta, Maya; Srivastava, Santosh
- Abstract
Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian estimates, depend on the accuracy of the prior parameters, but example simulations show that the performance can be substantially improved compared to maximum likelihood or state-of-the-art nonparametric estimators.
- Subjects
ENTROPY; BAYESIAN field theory; ESTIMATION theory; SYSTEMS theory; PARETO analysis; SIMULATION methods &; models; INVERSE Gaussian distribution; DISTRIBUTION (Probability theory); FREE probability theory
- Publication
Entropy, 2010, Vol 12, Issue 4, p818
- ISSN
1099-4300
- Publication type
Article
- DOI
10.3390/e12040818