{"title":"Exact Bayesian inference by symbolic disintegration","authors":"Chung-chieh Shan, N. Ramsey","doi":"10.1145/3009837.3009852","DOIUrl":null,"url":null,"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.","PeriodicalId":20657,"journal":{"name":"Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages","volume":"3 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"40","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3009837.3009852","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 40
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.