  Big Bayes is the computationally intensive co-application of big data and
large, expressive Bayesian models for the analysis of complex phenomena in
scientific inference and statistical learning. Standing as an example, Bayesian
multidimensional scaling (MDS) can help scientists learn viral trajectories
through space-time, but its computational burden prevents its wider use.
Crucial MDS model calculations scale quadratically in the number of
observations. We partially mitigate this limitation through massive
parallelization using multi-core central processing units, instruction-level
vectorization and graphics processing units (GPUs). Fitting the MDS model using
Hamiltonian Monte Carlo, GPUs can deliver more than 100-fold speedups over
serial calculations and thus extend Bayesian MDS to a big data setting. To
illustrate, we employ Bayesian MDS to infer the rate at which different
seasonal influenza virus subtypes use worldwide air traffic to spread around
the globe. We examine 5392 viral sequences and their associated 14 million
pairwise distances arising from the number of commercial airline seats per year
between viral sampling locations. To adjust for shared evolutionary history of
the viruses, we implement a phylogenetic extension to the MDS model and learn
that subtype H3N2 spreads most effectively, consistent with its epidemic
success relative to other seasonal influenza subtypes. Finally, we provide
MassiveMDS, an open-source, stand-alone C++ library and rudimentary R package,
and discuss program design and high-level implementation with an emphasis on
important aspects of computing architecture that become relevant at scale.
