Detecting changes in real-time data: a user's guide to optimal detection

P. Johnson, J. Moriarty, G. Peskir
2017 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
The real-time detection of changes in a noisily observed signal is an important problem in applied science and engineering. The study of parametric optimal detection theory began in the 1930s, motivated by applications in production and defence. Today this theory, which aims to minimise a given measure of detection delay under accuracy constraints, finds applications in domains including radar, sonar, seismic activity, global positioning, psychological testing, quality control, communications
more » ... d power systems engineering. This paper reviews developments in optimal detection theory and sequential analysis, including sequential hypothesis testing and change-point detection, in both Bayesian and classical (non-Bayesian) settings. For clarity of exposition we work in discrete time and provide a brief discussion of the continuous time setting, including recent developments using stochastic calculus. Different measures of detection delay are presented, together with the corresponding optimal solutions. We emphasise the important role of the signal-to-noise ratio and discuss both the underlying assumptions and some typical applications for each formulation.
doi:10.1098/rsta.2016.0298 pmid:29052544 pmcid:PMC5514354 fatcat:h7h7fae6onhjjjxwkodjrcuhhu