Statistical models of real world data typically involve continuous probability distributions such as normal, Laplace, or exponential distributions. Such distributions are supported by many probabilistic modelling formalisms, including probabilistic database systems. Yet, the traditional theoretical framework of probabilistic databases focuses entirely on finite probabilistic databases. Only recently, we set out to develop the mathematical theory of infinite probabilistic databases. The present paper is an exposition of two recent papers which are cornerstones of this theory. In (Grohe, Lindner; ICDT 2020) we propose a very general framework for probabilistic databases, possibly involving continuous probability distributions, and show that queries have a well-defined semantics in this framework. In (Grohe, Kaminski, Katoen, Lindner; PODS 2020) we extend the declarative probabilistic programming language Generative Datalog, proposed by (B´ar´any et al. 2017) for discrete probability distributions, to continuous probability distributions and show that such programs yield generative models of continuous probabilistic databases.

中文翻译：

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具有连续分布的概率数据

现实世界数据的统计模型通常涉及连续概率分布，例如正态分布、拉普拉斯分布或指数分布。这种分布得到许多概率建模形式的支持，包括概率数据库系统。然而，概率数据库的传统理论框架完全集中在有限概率数据库上。直到最近，我们才着手发展无限概率数据库的数学理论。本文是对作为该理论基石的最近两篇论文的阐述。在（Grohe，Lindner；ICDT 2020）中，我们提出了一个非常通用的概率数据库框架，可能涉及连续概率分布，并表明查询在该框架中具有明确定义的语义。在（高仪、卡明斯基、卡托恩、林德纳；