  Divide-and-conquer strategies for Monte Carlo algorithms are an increasingly
popular approach to making Bayesian inference scalable to large data sets. In
its simplest form, the data are partitioned across multiple computing cores and
a separate Markov chain Monte Carlo algorithm on each core targets the
associated partial posterior distribution, which we refer to as a
sub-posterior, that is the posterior given only the data from the segment of
the partition associated with that core. Divide-and-conquer techniques reduce
computational, memory and disk bottle-necks, but make it difficult to recombine
the sub-posterior samples. We propose SwISS: Sub-posteriors with Inflation,
Scaling and Shifting; a new approach for recombining the sub-posterior samples
which is simple to apply, scales to high-dimensional parameter spaces and
accurately approximates the original posterior distribution through affine
transformations of the sub-posterior samples. We prove that our transformation
is asymptotically optimal across a natural set of affine transformations and
illustrate the efficacy of SwISS against competing algorithms on synthetic and
real-world data sets.
