Article,
A Markov chain Monte Carlo expectation maximization algorithm for statistical analysis of DNA sequence evolution with neighbor-dependent substitution rates
Journal of Computational and Graphical Statistics, 17 (1): 138--162 (2008)
Abstract
The evolution of DNA sequences can be described by discrete state continuous time
Markov processes on a phylogenetic tree. We consider neighbor-dependent evolution-
ary models where the instantaneous rate of substitution at a site depends on the states
of the neighboring sites. Neighbor-dependent substitution models are analytically in-
tractable and must be analyzed using either approximate or simulation-based methods.
We describe statistical inference of neighbor-dependent models using a Markov chain
Monte Carlo expectation maximization (MCMC-EM) algorithm. In the MCMC-EM
algorithm, the high-dimensional integrals required in the EM algorithm are estimated
using MCMC sampling. The MCMC sampler requires simulation of sample paths from
a continuous time Markov process, conditional on the beginning and ending states and
the paths of the neighboring sites. An exact path sampling algorithm is developed for
this purpose.
