论文标题
随机过程网络引起的上下文情景
Contextuality scenarios arising from networks of stochastic processes
论文作者
论文摘要
经验模型是概率空间的概括。它由随机变量的X类的X类简单络合物组成，使每个单纯形具有相关的概率分布。随之而来的边缘化是连贯的，从某种意义上说，单纯形的分布与整个单纯形上的分布的边缘相吻合。 如果无法获得X上的联合分布的边缘分布，则可以说一个经验模型。上下文经验模型自然出现在量子理论中，从而产生其一些违反直觉的统计后果。 在本文中，我们提出了上下文经验模型的不同且经典的来源：许多随机过程之间的相互作用。我们将经验模型附加到随后的网络，在该网络中，每个节点代表带有输入和输出随机变量的开放随机过程。从长远来看，网络的统计行为使经验模型具有一般上下文，甚至是强烈的上下文。
An empirical model is a generalization of a probability space. It consists of a simplicial complex of subsets of a class X of random variables such that each simplex has an associated probability distribution. The ensuing marginalizations are coherent, in the sense that the distribution on a face of a simplex coincides with the marginal of the distribution over the entire simplex. An empirical model is said contextual if its distributions cannot be obtained marginalizing a joint distribution over X. Contextual empirical models arise naturally in quantum theory, giving rise to some of its counter-intuitive statistical consequences. In this paper we present a different and classical source of contextual empirical models: the interaction among many stochastic processes. We attach an empirical model to the ensuing network in which each node represents an open stochastic process with input and output random variables. The statistical behavior of the network in the long run makes the empirical model generically contextual and even strongly contextual.
