Non-Commutative Probability Models in Human Decision Making: Binary Hypothesis Testing

Abstract

Abstract In this paper, we consider the binary hypothesis testing problem, as the simplest human decision making problem, using a von-Neumann non-commutative probability framework. We present two approaches to this decision making problem. In the first approach, we represent the available data as coming from measurements modeled via projection valued measures (PVM) and retrieve the results of the underlying detection problem solved using classical probability models. In the second approach, we represent the measurements using positive operator valued measures (POVM). We prove that the minimum probability of error achieved in the second approach is the same as in the first approach.