Minimum Expected Relative Entropy Principle

0525233 - ÚTIA 2021 RIV RU eng C - Konferenční příspěvek (zahraniční konf.)
Kárný, Miroslav
Minimum Expected Relative Entropy Principle.
Proceedings of the 18th European Control Conference (ECC). Saint Petersburg: European Union Control Association (EUCA), 2020, s. 35-40. ISBN 978-390714401-5.
[The European Control Conference (ECC 2020). Saint Petersburg (RU), 12.05.2020-15.05.2020]
Grant CEP: GA MŠMT(CZ) LTC18075
Grant ostatní: The European Cooperation in Science and Technology (COST)(XE) CA16228
Institucionální podpora: RVO:67985556
Klíčová slova: minimum relative entropy principle * uncertain prior probability * forgetting * fully probabilistic design * abrupt parameter changes
Obor OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
http://library.utia.cas.cz/separaty/2020/AS/karny-0525233.pdf

Stochastic filtering estimates a timevarying (multivariate) parameter (a hidden variable) from noisy observations. It needs both observation and parameter evolution models. The latter is often missing or makes the estimation too complex. Then, the axiomatic minimum relative entropy (MRE) principle completes the posterior probability density (pd) of the parameter. The MRE principle recommends to modify a prior guess of the constructed pd to the smallest extent enforced by new observations. The MRE principle does not deal with a generic uncertain prior guess. Such uncertainty arises, for instance, when the MRE principle is used recursively. The paper fills this gap. The proposed minimum expected relative entropy (MeRE) principle: (a) makes Bayesian estimation less sensitive to the choice of the prior pd. (b) provides a stabilised parameter tracking with a data-dependent forgetting that copes with abrupt parameter changes. (c) applies in all cases exploiting MRE, for instance, in stochastic modelling.
Trvalý link: http://hdl.handle.net/11104/0309415