Abstract We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning and disintegration; various versions of conditional independence and its standard properties; conditional products; almost surely; sufficient statistics; versions of theorems on sufficient statistics due to Fisher–Neyman, Basu, and Bahadur. Besides the conceptual clarity offered by our categorical setup, its main advantage is that it provides a uniform treatment of various types of probability theory, including discrete probability theory, measure-theoretic probability with general measurable spaces, Gaussian probability, stochastic processes of either of these kinds, and many others.

中文翻译：

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马尔可夫核、条件独立性和充分统计定理的综合方法

摘要 我们根据 Golubtsov 以及 Cho 和 Jacobs 的工作，开发了马尔可夫类别作为合成概率和统计的框架。这意味着我们用纯粹抽象的分类术语来处理以下概念：条件作用和解体；各种版本的条件独立及其标准属性；有条件的产品；几乎可以肯定；足够的统计数据；由于 Fisher-Neyman、Basu 和 Bahadur，关于足够统计量的定理版本。除了我们的分类设置提供的概念清晰度之外，它的主要优点是它提供了对各种类型概率论的统一处理，包括离散概率论、具有一般可测量空间的测度论概率、高斯概率、这些概率的随机过程种类，以及许多其他。