Selective Probabilistic Causality as Interdisciplinary Methodology

这个项目将发展一个选择性概率因果关系的数学理论，用统计程序和经验说明来补充它。 该理论回答了这样一个问题：给定系统的一组输入和一组概率非独立的输出，如何确定每个输出受哪个输入的影响？ 该理论在行为、社会和健康科学中有应用。 例如，在联合测试中，是否学习时间或特定的培训，其中一个测试选择性地影响一个人的表现，在这个测试？ 在研究知觉判断时，对给定刺激属性的评估是否仅受该属性的选择性影响？ 或者在医学研究中，特定症状的存在或不存在是否选择性地取决于特定的疾病？ 该理论在量子力学中也有应用，解决了诸如带有局部非上下文变量的模型是否可以解释纠缠粒子系统中的自旋分布等问题。 该项目将对选择性的各种必要条件进行分类，并通过将每个条件几何表示为多维区域并测量其超体积来测量其相对强度。 该项目还将通过使用广义量子和经典概率形式主义对不同形式的选择性影响的违反进行分类和量化。 透过一系列的心理物理学实验，以“测试”的方式来说明所涉及的计算和分析，并阐明长期存在的心理学问题，如信号的可检测性和信号维度的感知可分离性。该项目旨在加深我们对因果关系和概率概念的理解，这些概念与决定论和自由意志等长期存在的问题有关。 当受影响的量是随机实体时，能够计算“什么影响什么”在科学、技术和医学的所有领域也具有重要的实际意义。 这些应用程序将得到在项目框架内开发的免费软件的便利。 该项目是跨学科的，国际性的，合作的，涉及两个国家的三所大学。 将在跨学科会议上组织一系列专题讨论会和讲习班。 与本项目相关的主题将用于研究生和本科生课程以及研究培训。

This project will develop a mathematical theory for selective probabilistic causality, complementing it with statistical procedures and empirical illustrations. The theory answers the question: Given a set of inputs into a system and a set of probabilistic non-independent outputs, how can one determine, for each of the outputs, which of the inputs it is influenced by? The theory has applications in behavioral, social, and health sciences. For example, in conjoint testing, does study time or specific training for one of the tests selectively influence one's performance in this test only? In studying perceptual judgments, is an assessment of a given stimulus property selectively influenced by this property alone? Or in medical research, does the presence or absence of a given symptom selectively depend on a given illness? The theory also has applications in quantum mechanics, addressing such questions as whether a model with local non-contextual variables can account for the distribution of spins in a system of entangled particles. The project will classify various necessary conditions for selectiveness and measure their comparative strength by geometrically representing each condition as a multidimensional region and measuring its hypervolume. The project also will classify and quantify different forms of violations of selective influences by means of using generalized quantum and classical probabilistic formalisms. A series of psychophysical experiments will be conducted to "test-drive" and illustrate the computations and analyses involved, as well as elucidate the long-standing psychological problems of signal detectability and perceptual separability of signal's dimensions.The project is aimed at deepening our understanding of the notions of causality and probability, bearing on such perennial issues as determinism and free will. Being able to compute "what influences what" when the influenced quantities are random entities is also of great practical importance in all spheres of science, technology, and medicine. These applications will be facilitated by the freely available software to be developed within the framework of the project. The project is interdisciplinary, international, and collaborative, involving three universities in two countries. A series of symposia and workshops will be organized at interdisciplinary conferences. Topics related to this project will be used in graduate and undergraduate courses as well as in research training.