Estimation of the Suspicious Observations Center*

Krzysztof Szajowski
unpublished
The paper extends the results on the problem of change point detection for Markov processes generalizing the results contained in the publications [11], [15] and [8]. The short description are as follows. A random sequence having segments being the homogeneous Markov processes is registered. Each segment has his own transition probability law and the length of the segment is unknown and random. The transition probabilities of each process are known and joint a priori distribution of the
more » ... tion of the disorder moments are given. The detection of the disorder rarely is precise. The decision maker accepts some deviation in estimation of the disorder moments. In this note the aim is to indicate the segment of given length between disorders with maximal probabilities. The case with various precision for over and under estimation of the middle point is analyzed including situation when the disorders do not appear with positive probability is also included. The observed sequence, when the change point is known, has the Markov properties. The results explain the structure of optimal detector in various circumstances and shows new details of the solution construction as well insignificantly extends range of application. The motivation for this investigation is the modeling of selection the suspicious observations in the experiments. Such observation can be treated as outliers or disturbed. The objectives is to detect such inaccuracy immediately or in very short time before or after it appearance with highest probability. The problem is reformulated to optimal stopping of the observed sequences. The detailed analysis of the problem is presented to show the form of optimal decision function. The application of the results to analysis of piecewise deterministic processes with change points appearing at the moment of jumps is shown (see [6], [10], [5]).
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