DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**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

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491