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.

Rev. C) Statistical modeling of nuclear data provides a novel approach to nuclear systematics complementary to established theoretical and phenomenological approaches based on quantum theory. More specifically, fully-connected, multilayer feedforward artificial neural network models are developed using the Levenberg-Marquardt optimization algorithm together with Bayesian regularization and cross-validation. The predictive performance of models emerging from extensive computer experiments is compared with that of traditional microscopic and phenomenological models as well as with the performance of other learning systems, including earlier neural network models as well as the support vector machines recently applied to the same problem. In discussing the results, emphasis is placed on predictions for nuclei that are far from the stability line, and especially those involved in the r-process nucleosynthesis. It is found that the new statistical models can match or even surpass the predictive performance of conventional models for beta-decay systematics and accordingly should provide a valuable additional tool for exploring the expanding nuclear landscape. I. INTRODUCTION "Numbers are the within of all things." Among nuclear physicists this need is driven both by the experimental programs of existing and future radioactive ion beam facilities and by the stresses placed on established nuclear structure theory as totally new areas of the nuclear landscape are opened for exploration. For nuclear astrophysicists, such information is intrinsic to an understanding of supernova explosions - the initialization of the explosion, the subsequent neutronization of the core material, and the strength and fate of the shock wave formed - and the nucleosynthesis of heavy elements above Fe, notably the r-process [3, 4, 5]. Both the element distribution on the r-path and the time scale of the r-process are highly sensitive to the β-decay properties of the neutron-rich nuclei involved. Except for a few key nuclei, β decay of r-process nuclei cannot be studied in terrestrial laboratories, so the required information must come from nuclear models. These include the more phenomenological treatments, such as the Gross Theory (GT), as well as microscopic approaches based on the shell model and the proton-neutron Quasiparticle Random-Phase Approximation (pnQRPA) in various versions.