DeepAI

# Disintegration and Bayesian Inversion, Both Abstractly and Concretely

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.

• 4 publications
• 25 publications
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 ...
01/18/2013

### User Interface Tools for Navigation in Conditional Probability Tables and Elicitation of Probabilities in Bayesian Networks

Elicitation of probabilities is one of the most laborious tasks in build...
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...