Massive numerical integration plagues the statistical inference of

partially observed stochastic processes.  An important biological

example entertains partially observed continuous-time Markov chains

(CTMCs) to model molecular sequence evolution.  Joint inference of

phylogenetic trees and codon-based substitution models of sequence

evolution remains computationally impractical.  Parallelizing data

likelihood calculations is an obvious strategy; however, across a

cluster-computer, this scales with the total number of processing

cores, incurring considerable cost to achieve reasonable run-time.

To solve this problem, I describe many-core computing algorithms that

harness inexpensive graphics processing units (GPUs) for calculation

of the likelihood under CTMC models of evolution.  High-end GPUs

containing hundreds of cores and are low-cost.  These novel algorithms

are particularly efficient for large state-spaces, including codon

models, and large data sets, such as full genome alignments where we

demonstrate up to 150-fold speed-up.  I conclude with a discussion of the

future of many-core computing in statistics and touch upon recent

experiences with massively large and high-dimensional mixture models.