hetGPy: Heteroskedastic Gaussian Process Modeling in Python

Computer experiments are ubiquitous in the physical and social sciences.When experiments are time-consuming to run, emulator (or surrogate) models are often used to map the input-output response surface of the simulator, treating it as a black box.The workhorse function of emulator models is Gaussian process regression (GPR).GPs provide flexible, non-linear regression targets with good interpolation properties and uncertainty quantification.However, it is well-known that nave GPR scales cubically with input size, and specifically involves intensive computation of matrix determinants and solving linear systems when fitting hyperparameters (Garnett, 2023;Gramacy, 2020).Further, nave GPR with noisy observations typically assumes an independent, identically-distributed noise process, but many data-generating mechanisms, especially those found in stochastic computer simulation, exhibit non-equal variance noise (also known as heteroskedasticity) (Baker et al., 2020).The software package hetGP (Binois & Gramacy, 2021) alleviates both of these concerns when the dataset of interest contains multiple observations per location (i.e. a dataset of size has << unique input locations).The hetGP framework can calculate matrix inverses and determinants (and therefore the log likelihood and its gradients) on the order ( 3 ) rather than ( 3 ) time in the nave case (Binois et al., 2018).This is accomplished via multiple applications of the Woodbury matrix identity (Binois et al., 2018;Harville, 1997) and leveraging the replication structure.Further, hetGP also models the mean and noise processes as two coupled GPs, allowing smooth noise dynamics over parameter space (Binois et al.,