Fully probabilistic design of hierarchical Bayesian models

0463052 - ÚTIA 2017 RIV US eng J - Journal Article
Quinn, A. - Kárný, Miroslav - Guy, Tatiana Valentine
Fully probabilistic design of hierarchical Bayesian models.
Information Sciences. Roč. 369, č. 1 (2016), s. 532-547. ISSN 0020-0255. E-ISSN 1872-6291
R&D Projects: GA ČR GA13-13502S
Institutional support: RVO:67985556
Keywords : Fully probabilistic design * Ideal distribution * Minimum cross-entropy principle * Bayesian conditioning * Kullback-Leibler divergence * Bayesian nonparametric modelling
Subject RIV: BB - Applied Statistics, Operational Research
Impact factor: 4.832, year: 2016
http://library.utia.cas.cz/separaty/2016/AS/karny-0463052.pdf

The minimum cross-entropy principle is an established technique for design of an un- known distribution, processing linear functional constraints on the distribution. More generally, fully probabilistic design (FPD) chooses the distribution-within the knowledge-constrained set of possible distributions-for which the Kullback-Leibler divergence to the designer’s ideal distribution is minimized. These principles treat the unknown distribution deterministically. In this paper, fully probabilistic design is applied to hierarchical Bayesian models for the first time, yielding optimal design of a (possibly nonparametric) stochastic model for the unknown distribution. This equips minimum cross-entropy and FPD distributional estimates with measures of uncertainty. It enables robust choice of the optimal model, as well as randomization of this choice. The ability to process non-linear functional constraints in the constructed distribution significantly extends the applicability of these principles.
Permanent Link: http://hdl.handle.net/11104/0262369