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Insights into Entropy as a Measure of Multivariate Variability
Open AccessArticle

A Two-Stage Maximum Entropy Prior of Location Parameter with a Stochastic Multivariate Interval Constraint and Its Properties

Department of Statistics, Dongguk University-Seoul, Seoul 100-715, Korea
Academic Editor: Raúl Alcaraz Martínez
Entropy 2016, 18(5), 188; https://doi.org/10.3390/e18050188
Received: 25 January 2016 / Revised: 4 May 2016 / Accepted: 10 May 2016 / Published: 20 May 2016
(This article belongs to the Section Information Theory, Probability and Statistics)
This paper proposes a two-stage maximum entropy prior to elicit uncertainty regarding a multivariate interval constraint of the location parameter of a scale mixture of normal model. Using Shannon’s entropy, this study demonstrates how the prior, obtained by using two stages of a prior hierarchy, appropriately accounts for the information regarding the stochastic constraint and suggests an objective measure of the degree of belief in the stochastic constraint. The study also verifies that the proposed prior plays the role of bridging the gap between the canonical maximum entropy prior of the parameter with no interval constraint and that with a certain multivariate interval constraint. It is shown that the two-stage maximum entropy prior belongs to the family of rectangle screened normal distributions that is conjugate for samples from a normal distribution. Some properties of the prior density, useful for developing a Bayesian inference of the parameter with the stochastic constraint, are provided. We also propose a hierarchical constrained scale mixture of normal model (HCSMN), which uses the prior density to estimate the constrained location parameter of a scale mixture of normal model and demonstrates the scope of its applicability. View Full-Text
Keywords: hierarchical constrained scale mixture of normal model; rectangle-screened normal distribution; two-stage maximum entropy prior; uncertain constraint; 62H30; 62F15 hierarchical constrained scale mixture of normal model; rectangle-screened normal distribution; two-stage maximum entropy prior; uncertain constraint; 62H30; 62F15
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Kim, H.-J. A Two-Stage Maximum Entropy Prior of Location Parameter with a Stochastic Multivariate Interval Constraint and Its Properties. Entropy 2016, 18, 188.

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