  Gaussian processes (GPs) are commonly used for prediction and inference for
spatial data analyses. However, since estimation and prediction tasks have
cubic time and quadratic memory complexity in number of locations, GPs are
difficult to scale to large spatial datasets. The Vecchia approximation induces
sparsity in the dependence structure and is one of several methods proposed to
scale GP inference. Our work adds to the substantial research in this area by
developing a stochastic gradient Markov chain Monte Carlo (SGMCMC) framework
for efficient computation in GPs. At each step, the algorithm subsamples a
minibatch of locations and subsequently updates process parameters through a
Vecchia-approximated GP likelihood. Since the Vecchia-approximated GP has a
time complexity that is linear in the number of locations, this results in
scalable estimation in GPs. Through simulation studies, we demonstrate that
SGMCMC is competitive with state-of-the-art scalable GP algorithms in terms of
computational time and parameter estimation. An application of our method is
also provided using the Argo dataset of ocean temperature measurements.
