DeepAI AI Chat
Log In Sign Up

Order Effects of Measurements in Multi-Agent Hypothesis Testing

by   Aneesh Raghavan, et al.
University of Maryland

All propositions from the set of events for an agent in a multi-agent system might not be simultaneously verifiable. In this paper, we revisit the concepts of event-state-operation structure and relationship of incompatibility from literature and use them as a tool to study the algebraic structure of the set of events. We present an example from multi-agent hypothesis testing where the set of events does not form a Boolean algebra but forms an ortholattice. A possible construction of a 'noncommutative probability space', accounting for incompatible events (events which cannot be simultaneously verified) is discussed. As a possible decision-making problem in such a probability space, we consider the binary hypothesis testing problem. 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.


Minimum Probability of Error of List M-ary Hypothesis Testing

We study a variation of Bayesian M-ary hypothesis testing in which the t...

Active Hypothesis Testing: Beyond Chernoff-Stein

An active hypothesis testing problem is formulated. In this problem, the...

Interpolating between symmetric and asymmetric hypothesis testing

The task of binary quantum hypothesis testing is to determine the state ...

Towards the Design of Prospect-Theory based Human Decision Rules for Hypothesis Testing

Detection rules have traditionally been designed for rational agents tha...

CT-NOR: Representing and Reasoning About Events in Continuous Time

We present a generative model for representing and reasoning about the r...

Process, Structure, and Modularity in Reasoning with Uncertainty

Computational mechanisms for uncertainty management must support interac...