  In environmental studies, realistic simulations are essential for
understanding complex systems. Statistical emulation with Gaussian processes
(GPs) in functional data models have become a standard tool for this purpose.
Traditional centralized processing of such models requires substantial
computational and storage resources, leading to emerging distributed Bayesian
learning algorithms that partition data into shards for distributed
computations. However, concerns about the sensitivity of distributed inference
to shard selection arise. Instead of using data shards, our approach employs
multiple random matrices to create random linear projections, or sketches, of
the dataset. Posterior inference on functional data models is conducted using
random data sketches on various machines in parallel. These individual
inferences are combined across machines at a central server. The aggregation of
inference across random matrices makes our approach resilient to the selection
of data sketches, resulting in robust distributed Bayesian learning. An
important advantage is its ability to maintain the privacy of sampling units,
as random sketches prevent the recovery of raw data. We highlight the
significance of our approach through simulation examples and showcase the
performance of our approach as an emulator using surrogates of the Sea, Lake,
and Overland Surges from Hurricanes (SLOSH) simulator - an important simulator
for government agencies.
