@article{heunen_convenient_2017,
title = {A {Convenient} {Category} for {Higher}-{Order} {Probability} {Theory}},
url = {http://arxiv.org/abs/1701.02547},
abstract = {Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of probability theory. Programs may use both higher-order functions and continuous distributions, or even define a probability distribution on functions. But standard probability theory does not handle higher-order functions well: the category of measurable spaces is not cartesian closed. Here we introduce quasi-Borel spaces. We show that these spaces: form a new formalization of probability theory replacing measurable spaces; form a cartesian closed category and so support higher-order functions; form a well-pointed category and so support good proof principles for equational reasoning; and support continuous probability distributions. We demonstrate the use of quasi-Borel spaces for higher-order functions and probability by: showing that a well-known construction of probability theory involving random functions gains a cleaner expression; and generalizing de Finetti's theorem, that is a crucial theorem in probability theory, to quasi-Borel spaces.},
urldate = {2019-10-10},
journal = {arXiv:1701.02547 [cs, math]},
author = {Heunen, Chris and Kammar, Ohad and Staton, Sam and Yang, Hongseok},
month = jan,
year = {2017},
note = {arXiv: 1701.02547}
}