Quickest Change Detection In Multiple On-off Processes: Switching With Memory

Abstract—We consider the quickest detection of idle periods in multiple on-off processes. At each time, only one process can be observed, and the observations are random realizations drawn from two different distributions depending on the current state (on or off) of the chosen process. Switching back to a previously visited process is allowed, and measurements obtained during previous visits are taken into account in decision making. The objective is to catch an idle period in any of the on-off processes as quickly as possible subject to a constraint on the probability of mistaking a busy period for an idle one. Assuming geometrically distributed busy and idle times, we establish a Bayesian formulation of the problem within a decisiontheoretic framework. Basic structures of the optimal decision rules are established. Based on these basic structures, we propose a low-complexity threshold policy for switching among processes and declaring idle periods. The near optimal performance of this threshold policy is demonstrated by a comparison with a genie-aided system which defines an upper bound on the optimal performance. This problem finds applications in spectrum opportunity detection in cognitive radio networks where a secondary user searches for idle channels in the spectrum. Index Terms—Quickest change detection, on-off process, spectrum opportunity detection, cognitive radio, genie-aided system I

Stochastic models of evidence accumulation in changing environments

Organisms and ecological groups accumulate evidence to make decisions. Classic experiments and theoretical studies have explored this process when the correct choice is fixed during each trial. However, we live in a constantly changing world. What effect does such impermanence have on classical results about decision making? To address this question we use sequential analysis to derive a tractable model of evidence accumulation when the correct option changes in time. Our analysis shows that ideal observers discount prior evidence at a rate determined by the volatility of the environment, and the dynamics of evidence accumulation is governed by the information gained over an average environmental epoch. A plausible neural implementation of an optimal observer in a changing environment shows that, in contrast to previous models, neural populations representing alternate choices are coupled through excitation. Our work builds a bridge between statistical decision making in volatile environments and stochastic nonlinear dynamics.Comment: 26 pages, 7 figure