  Fitting a theoretical model to experimental data in a Bayesian manner using
Markov chain Monte Carlo typically requires one to evaluate the model thousands
(or millions) of times. When the model is a slow-to-compute physics simulation,
Bayesian model fitting becomes infeasible. To remedy this, a second statistical
model that predicts the simulation output -- an "emulator" -- can be used in
lieu of the full simulation during model fitting. A typical emulator of choice
is the Gaussian process (GP), a flexible, non-linear model that provides both a
predictive mean and variance at each input point. Gaussian process regression
works well for small amounts of training data ($n < 10^3$), but becomes slow to
train and use for prediction when the data set size becomes large. Various
methods can be used to speed up the Gaussian process in the medium-to-large
data set regime ($n > 10^5$), trading away predictive accuracy for drastically
reduced runtime. This work examines the accuracy-runtime trade-off of several
approximate Gaussian process models -- the sparse variational GP, stochastic
variational GP, and deep kernel learned GP -- when emulating the predictions of
density functional theory (DFT) models. Additionally, we use the emulators to
calibrate, in a Bayesian manner, the DFT model parameters using observed data,
resolving the computational barrier imposed by the data set size, and compare
calibration results to previous work. The utility of these calibrated DFT
models is to make predictions, based on observed data, about the properties of
experimentally unobserved nuclides of interest e.g. super-heavy nuclei.
