Selective Probabilistic Causality as Interdisciplinary Methodology

Purdue University, West Lafayette IN

Investigators

Abstract

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.