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seminars:stat:141009 [2014/09/25 20:38] – created qiaoseminars:stat:141009 [2014/10/04 14:30] (current) – qyu
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 +<WRAP centeralign>##Statistics Seminar##\\ Department of Mathematical Sciences</WRAP>
 +
 +~~META:title =October 9, 2014~~
 +<WRAP 70% center>
 +|  **DATE:**|Thursday, October 9, 2014 |
 +|  **TIME:**|1:15pm to 2:15pm |
 +|  **PLACE:**|OW 100E |
 +|  **SPEAKER:**|Grigory Sokolov (Binghamton University) |
 +|  **TITLE:**|On the Pre-Change Transition Probability Density of the Generalized Shiryaev--Roberts Change-Point Detection Procedure's Statistic in the Minimax Brownian Motion Setup|
 +</WRAP>
 +\\ 
 +
 +<WRAP center box 80%>
 +<WRAP centeralign>**Abstract**</WRAP>
 +We consider the problem of quickest change-point detection in continuous
 +time where the observed is a standard Brownian motion that may, at an
 +unknown moment in time, gain a persistent drift of a specified magnitude,
 +and the objective is to as quickly and as reliably as possible detect the
 +onset of the drift. Within this context, the specific focus is on the
 +emerging Generalized Shiryaev-Roberts (GSR) detection procedure. We derive
 +a closed-form formula for the pre-change transition probability density of
 +the diffusion process associated with the GSR decision statistic; the
 +transition probability density formula is found through direct solution of
 +the respective Kolmogorov forward equation (otherwise also known as the
 +Fokker--Planck equation, and closely connected to the Smoluchowski equation
 +and the Schrödinger equation from physics) via the Fourier spectral method.
 +To conclude, we exploit the obtained formulae numerically and offer a brief
 +study of the GSR statistic's behavior in the pre-change regime.
 +
 +This work (and in particular the methodology employed in it) may help gain
 +greater insight into the characteristics of the GSR procedure in continuous
 +time and thus foster and facilitate further research on both theoretical
 +and applied change-point detection.
 +
 +This is joint work with Aleksey Polunchenko (SUNY Binghamton).
 +
 +</WRAP>