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arXiv · 2101.00956

Computable Random Variables and Conditioning

Pieter Collins
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Abstract

The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets, and extends existing work in this area by providing a computable theory of conditional random variables. The theory is based within the framework of type-two effectivity, so has an explicit direct link with Turing computation, and is expressed in a system of computable types and operations, so has a clean mathematical description.

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Pieter Collins. 2020-12-22. Computable Random Variables and Conditioning. https://arxiv.org/abs/2101.00956

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