Cooperative Hypothesis Testing by Two Observers with Asymmetric Information
Aneesh Raghavan, John S. Baras
TL;DR
It has been shown that if the observations collected by the observers are independent conditioned on the hypothesis, then the minimum probability that the two observers agree and are wrong in the decentralized approach is upper bounded by theminimum probability of error achieved in the centralized approach.
Abstract
We consider the binary hypothesis testing problem with two observers. There are two possible states of nature (or hypotheses). Observations collected by the two observers are statistically related to the true state of nature. The knowledge of joint distribution of the observations collected and the true state of nature is unknown to the observers. There are two problems to be solved by the observers: (i) true state of nature is known: find the distribution of the local information collected; (ii) true state of nature is unknown: collaboratively estimate the same using the distributions found by solving the first problem. We present four algorithms, each having two phases where the two problems are solved, with emphasis on the information exchange between the observers and resulting patterns. We prove different properties of the algorithms including the following: the probability spaces constructed as a consequence of solving the first problem are dependent on the information patterns at the observers; (ii) the rate of decay of probability of error of algorithms while solving the second problem is dependent on the information exchange between the observers. We present a numerical example demonstrating the four algorithms.