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Entropy 2017, 19(12), 687; https://doi.org/10.3390/e19120687

Choosing between Higher Moment Maximum Entropy Models and Its Application to Homogeneous Point Processes with Random Effects

1
Department of Management Sciences, HEC Montréal, 3000, Chemin de la Côte-Sainte-Catherine, Montréal, QC H3T 2A7, Canada
2
Department of Mathematics, Université du Québec à Montréal, 201, Avenue du Président-Kennedy, Montréal, QC H2X 3Y7, Canada
*
Author to whom correspondence should be addressed.
Received: 29 August 2017 / Revised: 7 December 2017 / Accepted: 9 December 2017 / Published: 14 December 2017
(This article belongs to the Special Issue Maximum Entropy and Bayesian Methods)
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Abstract

In the Bayesian framework, the usual choice of prior in the prediction of homogeneous Poisson processes with random effects is the gamma one. Here, we propose the use of higher order maximum entropy priors. Their advantage is illustrated in a simulation study and the choice of the best order is established by two goodness-of-fit criteria: Kullback–Leibler divergence and a discrepancy measure. This procedure is illustrated on a warranty data set from the automobile industry. View Full-Text
Keywords: recurrent events; mixed-Poisson; the maximum entropy principle; moment matching; maximum likelihood estimation; discrepancy measure; Kullback–Leibler divergence; likelihood ratio test; mean square prediction error recurrent events; mixed-Poisson; the maximum entropy principle; moment matching; maximum likelihood estimation; discrepancy measure; Kullback–Leibler divergence; likelihood ratio test; mean square prediction error
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Khribi, L.; MacGibbon, B.; Fredette, M. Choosing between Higher Moment Maximum Entropy Models and Its Application to Homogeneous Point Processes with Random Effects. Entropy 2017, 19, 687.

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