Exact Bayesian inference by symbolic disintegration
Exact Bayesian inference by symbolic disintegration
复制标题
通过符号分解进行精确贝叶斯推理
DOI：
10.1145/3009837.3009852
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
N. Ramsey
中科院分区：
文献类型：
--
作者：
Chung;N. Ramsey
贝叶斯推理，从先验知识和观察到的证据的后验知识，通常由贝叶斯规则定义，即后验乘以观察的概率等于联合概率。但是，连续量的观测值的概率通常为零，在这种情况下，贝叶斯规则只说未知数乘以零就是零。为了从零概率观测值中推断出后验分布，分解的统计概念告诉我们将观测值指定为表达式而不是谓词，但没有告诉我们如何计算后验分布。我们提出的第一种方法计算的解体从概率的程序和一个数量的表达被观察到，即使当观察的概率为零。由于该方法产生一个精确的后验项，并保留一元项表示措施的语义，它组成了一个模块化的方式与其他推理方法，而不牺牲精度或性能。
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.