DeepAI AI Chat
Log In Sign Up

Disintegration and Bayesian Inversion, Both Abstractly and Concretely

08/29/2017
by   Kenta Cho, et al.
0

The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measure-theoretic probability --- via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several non-trivial examples.

READ FULL TEXT

page 14

page 15

page 31

page 32

page 36

07/22/2019

Conditional probability in Renyi spaces

In 1933 Kolmogorov constructed a general theory that defines the modern ...
09/07/2021

An Inversion Tool for Conditional Term Rewriting Systems – A Case Study of Ackermann Inversion

We report on an inversion tool for a class of oriented conditional const...
12/04/2018

Statistics with improper posteriors

In 1933 Kolmogorov constructed a general theory that defines the modern ...
01/12/2020

Asymptotic inversion of the binomial and negative binomial cumulative distribution functions

The computation and inversion of the binomial and negative binomial cumu...
03/08/2000

Hypothetical revision and matter-of-fact supposition

The paper studies the notion of supposition encoded in non-Archimedean c...
06/24/2016

Standard State Space Models of Unawareness (Extended Abstract)

The impossibility theorem of Dekel, Lipman and Rustichini has been thoug...