Abstract
We generalize the classic change-point problem to a "change-set" framework: a spatial Poisson process changes its intensity on an unobservable random set. Optimal detection of the set is defined by maximizing the expected value of a gain function. In the case that the unknown change-set is defined by a locally finite set of incomparable points, we present a sufficient condition for optimal detection of the set using multiparameter martingale techniques. Two examples are discussed.
Original language | English |
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Pages (from-to) | 640-659 |
Number of pages | 20 |
Journal | Annals of Applied Probability |
Volume | 20 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2010 |
Keywords
- Change-set
- Likelihood function
- Optimal stopping
- Point process
- Poisson process
- Sequential detection problem
- Smooth semi-martingale
- Stopping set