Statistical maps: A categorical approach

Mathematica Slovaca

Roman Frič¹ 

关键词: D-poset of fuzzy sets;    fuzzy probability;    measurable map;    probability measure;    statistical map;    product of probability spaces;    extended probability space;    extended random map;    transportation of probabilities;    conditional probability;   

DOI  :  10.2478/s12175-007-0013-8

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

In probability theory, each random variable f can be viewed as channel through which the probability p of the original probability space is transported to the distribution p f, a probability measure on the real Borel sets. In the realm of fuzzy probability theory, fuzzy probability measures (equivalently states) are transported via statistical maps (equivalently, fuzzy random variables, operational random variables, Markov kernels, observables). We deal with categorical aspects of the transportation of (fuzzy) probability measures on one measurable space into probability measures on another measurable spaces. A key role is played by D-posets (equivalently effect algebras) of fuzzy sets.

【 授权许可】

Unknown