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Statistical maps: A categorical approach

Research paper by Roman Frič

Indexed on: 01 Feb '07Published on: 01 Feb '07Published in: Mathematica Slovaca



Abstract

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 pf, 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.