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SUMMARY:Precision of Disorders Detection - Szajowski\, K (Wroclaw Universi
 ty of Technology)
DTSTART:20140115T163000Z
DTEND:20140115T170000Z
UID:TALK49919@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The lecture presents the results on the problem of change poin
 t detection\nfor Markov processes generalizing the results contained in th
 e publications [2]\, [4]\, [3] and [1]. The short description are as follo
 ws. A random sequence having segments being the homogeneous Markov process
 es is registered. Each segment has his own transition probability law and 
 the length of the segment is unknown and random. The transition probabilit
 ies of each process are known and joint a priori distribution of the disor
 der moments is given. The detection of the disorder rarely is precise. The
  decision maker accepts some deviation in estimation of the disorder momen
 t. In the models taken into account the aim is to indicate the change poin
 t with xed\, bounded error with maximal\nprobability. The case with vario
 us precision for over and under estimation of this point is analysed inclu
 ding situation when the disorder does not appears with positive probabilit
 y 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 c
 onstruction as well insignicantly extends range of application. The motiv
 ation for this investigation is the modelling of the attacks in the\nnode 
 of networks. The objectives is to detect one of the attack 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 op
 timal decision function.\n\nKey Words: disorder problem\, sequential detec
 tion\, optimal stopping\, multi-variate optimization\n
LOCATION:Seminar Room 1\, Newton Institute
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