Title: Bayesian estimation of a generalised entropy functional using alternative Dirichlet priors
Authors: JT Ferreira - University of Pretoria (South Africa) [presenting]
Andriette Bekker - University of Pretoria (South Africa)
Abstract: Entropy (of which Shannon's is arguably most popular) is a common and widely studied measurement of information contained within a system. Entropy is most often defined as a functional of a probability structure, and the practical problem of estimating entropy from (sometimes small) samples in many applied settings remains a challenging and relevant problem. Previously unconsidered Dirichlet generators are introduced as possible priors for an underlying countably discrete model (in particular, the multinomial model). Resultant estimators for the generalised entropy $H(p)$, which include popular entropy choices, under the considered priors and assuming squared error loss are derived and studied. Particular cases of these proposed priors will be of interest, and their effect on the estimation of the generalised entropy subject to different parameter scenarios will be investigated.