Probabilistic morphisms and Bayesian nonparametrics
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00541937" target="_blank" >RIV/67985840:_____/21:00541937 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1140/epjp/s13360-021-01427-7" target="_blank" >https://doi.org/10.1140/epjp/s13360-021-01427-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1140/epjp/s13360-021-01427-7" target="_blank" >10.1140/epjp/s13360-021-01427-7</a>
Alternative languages
Result language
angličtina
Original language name
Probabilistic morphisms and Bayesian nonparametrics
Original language description
In this paper we develop a functorial language of probabilistic morphisms and apply it to some basic problems in Bayesian nonparametrics. First we extend and unify the Kleisli category of probabilistic morphisms proposed by Lawvere and Giry with the category of statistical models proposed by Chentsov and Morse–Sacksteder. Then we introduce the notion of a Bayesian statistical model that formalizes the notion of a parameter space with a given prior distribution in Bayesian statistics. We revisit the existence of a posterior distribution, using probabilistic morphisms. In particular, we give an explicit formula for posterior distributions of the Bayesian statistical model, assuming that the underlying parameter space is a Souslin space and the sample space is a subset in a complete connected finite dimensional Riemannian manifold. Then we give a new proof of the existence of Dirichlet measures over any measurable space using a functorial property of the Dirichlet map constructed by Sethuraman.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GC18-01953J" target="_blank" >GC18-01953J: Geometric methods in statistical learning theory and applications</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
European Physical Journal Plus
ISSN
2190-5444
e-ISSN
2190-5444
Volume of the periodical
136
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
29
Pages from-to
441
UT code for WoS article
000647197900002
EID of the result in the Scopus database
2-s2.0-85104854782