A domain-theoretic framework for conditional probability and Bayesian updating in programming
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913675466506240 |
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| author | Di Gianantonio, Pietro Edalat, Abbas |
| author_facet | Di Gianantonio, Pietro Edalat, Abbas |
| contents | We present a domain-theoretic framework for probabilistic programming that provides a constructive definition of conditional probability and addresses computability challenges previously identified in the literature. We introduce a novel approach based on an observable notion of events that enables computability. We examine two methods for computing conditional probabilities -- one using conditional density functions and another using trace sampling with rejection -- and prove they yield consistent results within our framework. We implement these ideas in a simple probabilistic functional language with primitives for sampling and evaluation, providing both operational and denotational semantics and proving their consistency. Our work provides a rigorous foundation for implementing conditional probability in probabilistic programming languages. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_00949 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A domain-theoretic framework for conditional probability and Bayesian updating in programming Di Gianantonio, Pietro Edalat, Abbas Logic in Computer Science Programming Languages 03B70 F.3.2 We present a domain-theoretic framework for probabilistic programming that provides a constructive definition of conditional probability and addresses computability challenges previously identified in the literature. We introduce a novel approach based on an observable notion of events that enables computability. We examine two methods for computing conditional probabilities -- one using conditional density functions and another using trace sampling with rejection -- and prove they yield consistent results within our framework. We implement these ideas in a simple probabilistic functional language with primitives for sampling and evaluation, providing both operational and denotational semantics and proving their consistency. Our work provides a rigorous foundation for implementing conditional probability in probabilistic programming languages. |
| title | A domain-theoretic framework for conditional probability and Bayesian updating in programming |
| topic | Logic in Computer Science Programming Languages 03B70 F.3.2 |
| url | https://arxiv.org/abs/2502.00949 |