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<p>Our interest is the risk assessment of rare natural hazards, such as</p><p>large
volcanic pyroclastic flows. Since catastrophic consequences of</p><p>volcanic flows
are rare events, our analysis benefits from the use of</p><p>a computer model to provide
information about these events under</p><p>natural conditions that may not have been
observed in reality.</p><p>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.</p><p>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.</p><p>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.</p><p>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</p><p>to incorporate geophysical
information in the multivariate analysis of computer model output.</p>
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