Full metadata
Title
Bayesian Inference for Markov Kernels Valued in Wasserstein Spaces
Description
In this work, the author analyzes quantitative and structural aspects of Bayesian inference using Markov kernels, Wasserstein metrics, and Kantorovich monads. In particular, the author shows the following main results: first, that Markov kernels can be viewed as Borel measurable maps with values in a Wasserstein space; second, that the Disintegration Theorem can be interpreted as a literal equality of integrals using an original theory of integration for Markov kernels; third, that the Kantorovich monad can be defined for Wasserstein metrics of any order; and finally, that, under certain assumptions, a generalized Bayes’s Law for Markov kernels provably leads to convergence of the expected posterior distribution in the Wasserstein metric. These contributions provide a basis for studying further convergence, approximation, and stability properties of Bayesian inverse maps and inference processes using a unified theoretical framework that bridges between statistical inference, machine learning, and probabilistic programming semantics.
Date Created
2023
Contributors
- Eikenberry, Keenan (Author)
- Cochran, Douglas (Thesis advisor)
- Lan, Shiwei (Thesis advisor)
- Dasarathy, Gautam (Committee member)
- Kotschwar, Brett (Committee member)
- Shahbaba, Babak (Committee member)
- Arizona State University (Publisher)
Topical Subject
Resource Type
Extent
87 pages
Language
eng
Copyright Statement
In Copyright
Primary Member of
Peer-reviewed
No
Open Access
No
Handle
https://hdl.handle.net/2286/R.2.N.190789
Level of coding
minimal
Cataloging Standards
Note
Partial requirement for: Ph.D., Arizona State University, 2023
Field of study: Mathematics
System Created
- 2023-12-14 01:22:21
System Modified
- 2023-12-14 01:22:27
- 11 months 2 weeks ago
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