Abstract:  A useful definition of "big data" is data that is too big to comfortably process on a single
machine, either because of processor, memory, or disk bottlenecks. Graphics processing units
can alleviate the processor bottleneck, but memory or disk bottlenecks can only be eliminated
by splitting data across multiple machines. Communication between large numbers of machines
is expensive (regardless of the amount of data being communicated), so there is a need for
algorithms that perform distributed approximate Bayesian analyses with minimal communication.
Consensus Monte Carlo operates by running a separate Monte Carlo algorithm on each
machine, and then averaging individual Monte Carlo draws across machines. Depending on the
model, the resulting draws can be nearly indistinguishable from the draws that would have been
obtained by running a single machine algorithm for a very long time. Examples of consensus
Monte Carlo are shown for simple models where single-machine solutions are available, for large
single-layer hierarchical models, and for Bayesian additive regression trees (BART).