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.
Wed 18 Jan (GMT+02:00) Amsterdam, Berlin, Bern, Rome, Stockholm, Vienna change
|14:20 - 14:45|
Leonidas LampropoulosUniversity of Pennsylvania, Diane Gallois-WongInria Paris, ENS Paris, Cătălin HriţcuInria Paris, John HughesChalmers University of Technology, Benjamin C. PierceUniversity of Pennsylvania, Li-yao XiaENS ParisPre-print
|14:45 - 15:10|
|15:10 - 15:35|
|15:35 - 16:00|