Publication detail

On Bayesian Decision-Making and Approximation of Probability Densities

PAPEŽ, M.

Original Title

On Bayesian Decision-Making and Approximation of Probability Densities

English Title

On Bayesian Decision-Making and Approximation of Probability Densities

Type

conference paper

Language

en

Original Abstract

An approximation of a true, unknown, posterior probability density (pd) representing some real state-space systém is presented as Bayesian decision-making among a set of possible descriptions (models). The decision problem is carefully defined on its basic elements and it is shown how it leads to the use of the Kullback-Leibler (KL) divergence for evaluating a loss of information between the unknown posterior pd and its approximation. The resulting algorithm is derived on a general level, allowing specific algorithms to be designed according to a selected class of the probability distributions. A concrete example of the algorithm is proposed for the Gaussian case. An experiment is performed assuming that none of the possible descriptions is precisely identical with the unknown system.

English abstract

An approximation of a true, unknown, posterior probability density (pd) representing some real state-space systém is presented as Bayesian decision-making among a set of possible descriptions (models). The decision problem is carefully defined on its basic elements and it is shown how it leads to the use of the Kullback-Leibler (KL) divergence for evaluating a loss of information between the unknown posterior pd and its approximation. The resulting algorithm is derived on a general level, allowing specific algorithms to be designed according to a selected class of the probability distributions. A concrete example of the algorithm is proposed for the Gaussian case. An experiment is performed assuming that none of the possible descriptions is precisely identical with the unknown system.

Keywords

Bayesian inference, Bayesian filtering, Bayesian decision-making, probability density, Kullback-Leibler divergence.

RIV year

2015

Released

09.07.2015

Publisher

Institute of Electrical and Electronics Engineers

Location

Prague

ISBN

978-1-4799-8498-5

Book

38th International Conference on Telecommunications and Signal Processing (TSP)

Pages from

499

Pages to

503

Pages count

5

URL

Documents

BibTex


@inproceedings{BUT114323,
  author="Milan {Papež}",
  title="On Bayesian Decision-Making and Approximation of Probability Densities",
  annote="An approximation of a true, unknown, posterior probability density (pd) representing some real state-space systém is presented as Bayesian decision-making among a set of possible descriptions (models). The decision problem is carefully defined on its basic elements and it is shown how it leads to the use of the Kullback-Leibler (KL) divergence for evaluating a loss of information between the unknown posterior pd and its approximation. The resulting algorithm is derived on a general level, allowing specific algorithms to be designed according to a selected class of the probability distributions. A concrete example of the algorithm is proposed for the Gaussian case. An experiment is performed assuming that none of the possible descriptions is precisely identical with the unknown system.",
  address="Institute of Electrical and Electronics Engineers",
  booktitle="38th International Conference on Telecommunications and Signal Processing (TSP)",
  chapter="114323",
  doi="10.1109/TSP.2015.7296313",
  howpublished="electronic, physical medium",
  institution="Institute of Electrical and Electronics Engineers",
  year="2015",
  month="july",
  pages="499--503",
  publisher="Institute of Electrical and Electronics Engineers",
  type="conference paper"
}