Exact Bayesian inference by symbolic disintegration
Abstract
Bayesian inference, of posterior knowledge from prior knowledge and observed evidence, is typically defined by Bayes's rule, which says the posterior multiplied by the probability of an observation equals a joint probability. But the observation of a continuous quantity usually has probability zero, in which case Bayes's rule says only that the unknown times zero is zero. To infer a posterior distribution from a zero-probability observation, the statistical notion of disintegration tells us to specify the observation as an expression rather than a predicate, but does not tell us how to compute the posterior. We present the first method of computing a disintegration from a probabilistic program and an expression of a quantity to be observed, even when the observation has probability zero. Because the method produces an exact posterior term and preserves a semantics in which monadic terms denote measures, it composes with other inference methods in a modular way-without sacrificing accuracy or performance.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 01, 2017
- Source ID
- 10.1145/3093333.3009852
Entities
People
- Chung-chieh Shan
- Norman Ramsey
Organizations
- Defense Advanced Research Projects Agency
- Indiana University
- Lilly Endowment
- National Science Foundation
- Tufts University