On the Bayesian calibration of expensive computer models with input dependent parameters

Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model inputs. In several real world applications where models involve complex parametrizations whose optimal values depend on the model inputs, such an assumption can be too restrictive and may lead to misleading results. We propose a fully Bayesian methodology that produces input dependent optimal values for the calibration parameters, as well as it characterizes the associated uncertainties via posterior distributions. Central to methodology is the idea of formulating the calibration parameter as a step function whose uncertain structure is modeled properly via a binary treed process. Our method is particularly suitable to address problems where the computer model requires the selection of a sub-model from a set of competing ones, but the choice of the ‘best’ sub-model may change with the input values. The method produces a selection probability for each sub-model given the input. We propose suitable reversible jump operations to facilitate the challenging computations. We assess the performance of our method against benchmark examples, and use it to analyze a real world application with a large-scale climate model

Ice Model Calibration using Semi-continuous Spatial Data

Rapid changes in Earth’s cryosphere caused by human activity can lead to significant environmental impacts. Computer models provide a useful tool for understanding the behavior and projecting the future of Arctic and Antarctic ice sheets. However, these models are typically subject to large parametric uncertainties due to poorly constrained model input parameters that govern the behavior of simulated ice sheets. Computer model calibration provides a formal statistical framework to infer parameters using observational data, and to quantify the uncertainty in projections due to the uncertainty in these parameters. Calibration of ice sheet models is often challenging because the relevant model output and observational data take the form of semi-continuous spatial data, with a point mass at zero and a right-skewed continuous distribution for positive values. Current calibration approaches cannot handle such data. Here we introduce a hierarchical latent variable model that handles binary spatial patterns and positive continuous spatial patterns as separate components. To overcome challenges due to high-dimensionality we use likelihood-based generalized principal component analysis to impose low-dimensional structures on the latent variables for spatial dependence. We apply our methodology to calibrate a physical model for the Antarctic ice sheet and demonstrate that we can overcome the aforementioned modeling and computational challenges. As a result of our calibration, we obtain improved future ice-volume change projections

Multifidelity computer model emulation with high‐dimensional output: An application to storm surge

Hurricane-driven storm surge is one of the most deadly and costly natural disasters, making precise quantification of the surge hazard of great importance. Surge hazard quantification is often performed through physics-based computer models of storm surges. Such computer models can be implemented with a wide range of fidelity levels, with computational burdens varying by several orders of magnitude due to the nature of the system. The threat posed by surge makes greater fidelity highly desirable, however, such models and their high-volume output tend to come at great computational cost, which can make detailed study of coastal flood hazards prohibitive. These needs make the development of an emulator combining high-dimensional output from multiple complex computer models with different fidelity levels important. We propose a parallel partial autoregressive cokriging model to predict highly accurate storm surges in a computationally efficient way over a large spatial domain. This emulator has the capability of predicting storm surges as accurately as a high-fidelity computer model given any storm characteristics over a large spatial domain