Fully probabilistic design of hierarchical Bayesian models
Result description
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.
Keywords
Fully probabilistic designIdeal distributionMinimum cross-entropy principleBayesian conditioningKullback-Leibler divergenceBayesian nonparametric modelling
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Fully probabilistic design of hierarchical Bayesian models
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BB - Applied statistics, operational research
OECD FORD branch
—
Result continuities
Project
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Information Sciences
ISSN
0020-0255
e-ISSN
—
Volume of the periodical
369
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
532-547
UT code for WoS article
000383292500035
EID of the result in the Scopus database
2-s2.0-84978967308
Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BB - Applied statistics, operational research
Year of implementation
2016