2021/01/19 by Swaraj Dash, Sam Staton · 10 citations
Computer Science · Mathematics · #Constraint Satisfaction and Optimization #Distributive property #Monad (category theory) #Morphism #Point (geometry) #Point process #Point processes and geometric inequalities #Probabilistic logic #Space (punctuation) #Stochastic processes and statistical mechanics #cs.LO #cs.PL
paper · pdf · doi:10.4204/eptcs.333.2
published in Electronic Proceedings in Theoretical Computer Science 333, 19-32 (Open Publishing Association) · In Proceedings ACT 2020, arXiv:2101.07888
openalex publication_date 2021/01/19 · arxiv created 2021/01/26 · arxiv updated 2021/01/27 · openalex created_date 2021/02/01 · openalex updated_date 2026/08/05
A point process on a space is a random bag of elements of that space. In this paper we explore programming with point processes in a monadic style. To this end we identify point processes on a space X with probability measures of bags of elements in X. We describe this view of point processes using the composition of the Giry and bag monads on the category of measurable spaces and functions and prove that this composition also forms a monad using a distributive law for monads. Finally, we define a morphism from a point process to its intensity measure, and show that this is a monad morphism. A special case of this monad morphism gives us Wald's Lemma, an identity used to calculate the expected value of the sum of a random number of random variables. Using our monad we define a range of point processes and point process operations and compositionally compute their corresponding intensity measures using the monad morphism.