October 28, 2011, Webb 1100

We develop a Monte Carlo method to solve continuous-time sequential detection problems that arise in models for quality control and surveillance. An unobserved signal X undergoes a disorder at an unknown time to a new unknown level. The controller?s aim is to detect and identify this disorder as quickly as possible by sequentially monitoring a given observation process Y. We adopt a Bayesian setup that translates the problem into a two-step procedure of (i) stochastic filtering followed by (ii) an optimal stopping objective. We consider joint Wiener and Poisson observation processes Y and a variety of Bayes risk criteria. Due to the general setting, the state of our model is the full infinite-dimensional posterior distribution of X. Our computational procedure is based on combining sequential Monte Carlo filtering procedures with the regression Monte Carlo method for high-dimensional optimal stopping problems. Results are illustrated with several numerical examples.

MIKE LUDKOVSKI has been an Assistant Professor in the UCSB Department of Statistics and Applied Probability since 2008. He received a B.Sc. from Simon Fraser U in British Columbia, Canada, a Ph.D. in Operations Research and Financial Engineering from Princeton U and was previously a term assistant professor at U of Michigan. His research interests are in stochastic control, financial mathematics and applied probability with applications ranging from stochastic games in resource management to sequential change detection and control in biosurveillance models.