  While Bayesian inference is the gold standard for uncertainty quantification
and propagation, its use within physical chemistry encounters formidable
computational barriers. These bottlenecks are magnified for modeling data with
many independent variables, such as X-ray/neutron scattering patterns and
electromagnetic spectra. To address this challenge, we apply a Bayesian
framework accelerated via local Gaussian process (LGP) surrogate models. We
show that the time-complexity of LGPs scales linearly in the number of
independent variables, in stark contrast to the computationally expensive cubic
scaling of conventional Gaussian processes. To illustrate the method, we
trained a LGP surrogate model on the experimental radial distribution function
of liquid neon, and observed a remarkable 288,000-fold speed-up compared to
molecular dynamics with insignificant loss in predictive accuracy. We conclude
that LGPs are robust and efficient surrogate models, poised to expand the
application of Bayesian inference in molecular simulations to a broad spectrum
of ever-advancing experimental data.
