Copyright 2014 imperial college press all rights

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Copyright © 2014. Imperial College Press. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law. EBSCO Publishing : eBook Collection (EBSCOhost) - printed on 2/16/2016 3:37 AM via CGC-GROUP OF COLLEGES (GHARUAN) AN: 779681 ; Heard, Nicholas, Adams, Niall M..; Data Analysis for Network Cyber-security Account: ns224671
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Rapid Detection of Attacks by Quickest Changepoint Detection Methods 41 Note the recursion R n +1 = (1 + R n ) L n +1 , n 0 , R 0 = 0 (2.7) (with the null initial condition). Pollak (1985) tweaked the procedure by starting it off at a ran- dom R Q A 0 whose distribution is the quasi-stationary distribution Q A = lim n →∞ P ( R n x | T SR ( A ) > n ) of the SR statistic R n and showed that the detection procedure that stops and raises an alarm at the first time when the statistic R Q A n crosses the level A , T Q A A = min n 1: R Q A n A , (2.8) minimizes (asymptotically as γ → ∞ ) to within o (1) the maximal expected delay SADD ( T ) over all stopping times that satisfy E T γ , where A is such that E T Q A A = γ . We will refer to this randomized SR procedure as the Shiryaev–Roberts–Pollak (SRP) procedure. Until recently, the question of whether the SRP procedure is exactly minimax with respect to Pollak’s expected delay measure SADD ( T ) (in the class of procedures C γ ) was open. Moustakides et al. (2011) presented numerical evidence that uniformly better procedures exist. They proposed to start the original SR procedure at a fixed (but specially designed) point R r 0 = r , 0 r < A , showing that, for certain values of r , the expected conditional delay E ν ( T r A ν | T r A > ν ) < E ν ( T Q A A ν | T Q A A > ν ) for all ν 0, where A and A are such that E T Q A A = E T r A . We will refer to the procedure T r A that starts from r to as the SR r procedure. Tartakovsky et al. (2012) showed that the SR r procedure with a specially designed r = r ( γ ) is third-order asymptotically minimax (i.e., to within o (1)) in the class of procedures C γ with E T γ as γ → ∞ . Polunchenko and Tartakovsky (2010, 2012) provided examples where the SR r procedure is strictly minimax. In a variety of surveillance applications, including intrusion detection, the detection procedure should be applied repeatedly . This requires speci- fication of a renewal mechanism after each alarm (false or true). The sim- plest renewal strategy is to restart from scratch, in which case the procedure becomes multi-cyclic with similar cycles (in a statistical sense) if the process is homogeneous. Furthermore, the most interesting scenario for our applica- tions is when a change (attack) occurs at a distant time horizon, i.e., long after surveillance begins. This naturally leads to a problem of detecting a distant change in a stationary background of false alarms (stationary Copyright © 2014. Imperial College Press. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.
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  • Spring '12
  • Kushal Kanwar
  • Graph Theory, Statistical hypothesis testing, Imperial College Press, applicable copyright law

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