Modeling and quickest detection of a rapidly approaching object

• Published in: Sequential analysis Vol. 42; no. 4; pp. 387 - 403
• Main Authors: Brucks, Tim, Banerjee, Taposh, Mishra, Rahul
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.10.2023; Taylor & Francis Ltd
• Subjects: Algorithms; Data collection; Decision making; Disasters; False alarms; Military applications; Minimax optimality; monotone likelihood ratio; nonstationary processes; quickest change detection; Statistics; stochastic dominance; Stochastic processes
• ISSN: 0747-4946; 1532-4176
• DOI: 10.1080/07474946.2023.2247020

The problem of detecting the presence of a signal that can lead to a disaster is studied. A decision-maker collects data sequentially over time. At some point in time, called the change point, the distribution of data changes. This change in distribution could be due to an event or a sudden arrival of an enemy object. If not detected quickly, this change can potentially cause a major disaster. In space and military applications, the values of the measurements can stochastically grow with time as the enemy object moves closer to the target. A new class of stochastic processes called "exploding processes" is introduced to model stochastically growing data. An algorithm is proposed and shown to be asymptotically optimal as the mean time to a false alarm goes to infinity.