Applied measure theory for probabilistic modeling.
Paper in proceeding, 2022

Probabilistic programming and statistical computing are vibrant areas in the development of the Julia programming language, but the underlying infrastructure dramatically predates recent developments. The goal of MeasureTheory.jl is to provide Julia with the right vocabulary and tools for these tasks. In the package we introduce a well-chosen set of notions from the
foundations of probability together with powerful combinators and transforms, giving a gentle introduction to the concepts in this article.
The task is foremost achieved by recognizing measure as the central object. This enables us to develop a proper concept of densities as objects relating measures with each others. As densities provide local perspective on measures, they are the key to efficient implementations.
The need to preserve this computationally so important locality leads to the new notion of locally-dominated measure, solving the so-called “base measure problem” and making work with densities and distributions in Julia easier and more flexible.

Julia, Measure theory, Probability

Author

Chad Scherrer

Informative Prior

Moritz Schauer

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

JuliaCon Proceedings

Vol. 2022 1

JuliaCon
Virtual; online, ,

Subject Categories

Probability Theory and Statistics

DOI

10.21105/jcon.00092

More information

Latest update

10/27/2023