论文标题
可代表的马尔可夫类别和分类概率中统计实验的比较
Representable Markov Categories and Comparison of Statistical Experiments in Categorical Probability
论文作者
论文摘要
马尔可夫类别是概率和统计基础数学基础的最新分类方法。在这里，通过说明和证明二阶随机优势的等效条件来提出这种方法，这是一种广泛使用的方式，可以通过其扩散比较概率分布。此外，我们通过陈述和证明经典的Blackwell-Sherman-Stein定理来比较马尔可夫类别中统计实验的理论基础。我们的版本不仅提供了有关证明的新见解，而且其抽象性质也使结果更加笼统，自动专门针对标准的Blackwell-Sherman-Stein定理，以测量理论的概率以及涉及先前依赖依赖性垃圾的贝叶斯版本。在此过程中，我们定义并表征了代表的马尔可夫类别，其中人们可以谈论Markov内核与分布空间或从分布空间中。我们通过探索马尔可夫类别与概率单元类别之间的关系来做到这一点。
Markov categories are a recent categorical approach to the mathematical foundations of probability and statistics. Here, this approach is advanced by stating and proving equivalent conditions for second-order stochastic dominance, a widely used way of comparing probability distributions by their spread. Furthermore, we lay foundation for the theory of comparing statistical experiments within Markov categories by stating and proving the classical Blackwell-Sherman-Stein Theorem. Our version not only offers new insight into the proof, but its abstract nature also makes the result more general, automatically specializing to the standard Blackwell-Sherman-Stein Theorem in measure-theoretic probability as well as a Bayesian version that involves prior-dependent garbling. Along the way, we define and characterize representable Markov categories, within which one can talk about Markov kernels to or from spaces of distributions. We do so by exploring the relation between Markov categories and Kleisli categories of probability monads.
