Speaker: John Spouge, NIH
Title: Markov renewal-success processes with a time lag

Abstract: Poisson approximations are relevant to renewal-success processes, when a rare event (a success) can occur independent within every renewal interval. Renewal-success models are therefore relevant to queuing, machine failure, insurance risk, and dam failure, to name just a few applications. A renewal-success heuristic is also relevant to the BLAST computer program, which biologists use more than once a second over the web to compare their query sequences to our databases at NCBI. In particular, an accurate BLAST p-value for short sequences requires a heuristic finite-size correction (FSC), to extend the accuracy of the relevant Poisson approximation to unusually short times. The mathematical theory of the finite-size correction (FSC) is now known for both discrete time and continuous renewal processes in the non-Markov case, but the BLAST heuristic requires a FSC for Markov renewal-success processes. I therefore present a FSC theorem for the Markov renewal-success processes based on the standard technique of embedding a regeneration points in the Markov process. As examples of improvements over standard Poisson approximations, I show numerical results from Markov-modulated coin tossing trials and the inexact simple repeats problem in biological sequences, as well as in the BLAST statistics themselves.

Time: Friday, Dec. 3, 2010, 1:30-2:30 p.m.

Place: Science and Tech I, Room 242

Department of Mathematical Sciences
George Mason University
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