University of Idaho
Department of Mathematics Colloquia
Thursday, February 21, 2008
3:30 p.m. in TLC 031
Refreshments in Brink 330 at 3:00
Efficient computations of Markov functionals lead to novel statistical procedures in evolutionary biology
by
Vladimir Minin
Department of Statistics
University of Washington
Abstract:
In genetics and evolutionary biology, mutations are often modeled as continuous-time Markov chains. In practice,
these Markov chains are observed only partially through a finite sample of genetic sequences. However,
statistical inference and hypothesis testing often require calculating probabilistic properties of
unobserved functionals of Markov evolutionary trajectories. I will discuss efficient numerical algorithms for two of such
functionals, evolutionary counting and reward processes. I will demonstrate how these algorithms can be applied to
robust estimation of genetic distances, testing co-evolution of two genetic traits, and mapping mutations onto evolutionary
histories (phylogenies). I will also describe how Markov functionals can be used to detect and remedy model misspecification
in evolutionary applications.