Thesis
A monadic theory of point processes
- Abstract:
- A point process on a space is a random bag of elements of that space. In this thesis we explore programming with point processes in a monadic style. To this end we identify finite point processes on a space X with probability measures on finite 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. We also explore distributive laws for infinite point processes, where an infinite point process on X is a random stream of elements in X. We show that while there is no distributive law showing the space of infinite point processes to be a monad, there is a weak distributive law, which can be derived relatively generically. In the second half of this thesis we look at applications of the point process monad. We show that there is a morphism of monads giving the intensity measure of point processes and use it to derive a discrete version of Wald's lemma, a standard result from probability theory. Finally we use our point process monad to give a semantics to queries on probabilistic databases, which are databases with noisy data.
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Authors
Contributors
+ Staton, S
- Institution:
- University of Oxford
- Division:
- MPLS
- Department:
- Computer Science
- Role:
- Supervisor
+ Kissinger, A
- Institution:
- University of Oxford
- Division:
- MPLS
- Department:
- Computer Science
- Role:
- Examiner
+ Dahlqvist, F
- Institution:
- Queen Mary University of London
- Role:
- Examiner
+ Department of Computer Science, University of Oxford
More from this funder
- Funder identifier:
- https://ror.org/052gg0110
- Funding agency for:
- Dash, S
- Programme:
- Teaching Assistant
- DOI:
- Type of award:
- DPhil
- Level of award:
- Doctoral
- Awarding institution:
- University of Oxford
- Language:
-
English
- Keywords:
- Deposit date:
-
2025-03-03
- ARK identifier:
Terms of use
- Copyright holder:
- Swaraj Dash
- Copyright date:
- 2023
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