Development and Implementation of Bayesian Computer Model Emulators
Our interest is the risk assessment of rare natural hazards, such as large volcanic pyroclastic flows. Since catastrophic consequences of volcanic flows are rare events, our analysis benefits from the use of a computer model to provide information about these events under natural conditions that may not have been observed in reality. A common problem in the analysis of computer experiments, however, is the high computational cost associated with each simulation of a complex physical process. We tackle this problem by using a statistical approximation (emulator) to predict the output of this computer model at untried values of inputs. Gaussian process response surface is a technique commonly used in these applications, because it is fast and easy to use in the analysis. We explore several aspects of the implementation of Gaussian process emulators in a Bayesian context. First, we propose an improvement for the implementation of the plug-in approach to Gaussian processes. Next, we also evaluate the performance of a spatial model for large data sets in the context of computer experiments. Computer model data can also be combined to field observations in order to calibrate the emulator and obtain statistical approximations to the computer model that are closer to reality. We present an application where we learn the joint distribution of inputs from field data and then bind this auxiliary information to the emulator in a calibration process. One of the outputs of our computer model is a surface of maximum volcanic flow height over some geographical area. We show how the topography of the volcano area plays an important role in determining the shape of this surface, and we propose methods to incorporate geophysical information in the multivariate analysis of computer model output.