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Robert Erhardt, University of North Carolina at Chapel Hill

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Approximate Bayesian Computing for Spatial Extremes
17 January 2012 from 4:00 PM to 5:30 PM
201 Thomas Building
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Statistical analysis of max-stable processes used to model spatial extremes
has been limited by the difficulty in calculating the joint likelihood function.  This
precludes all standard likelihood-based approaches, including Bayesian approaches. 
In this paper we present a Bayesian approach through the use of approximate Bayesian
computing.  This circumvents the need for a joint likelihood function by instead relying on
simulations from the (unavailable) likelihood.  This method is compared with an alternative
approach based on the composite likelihood.  When estimating the spatial dependence of
extremes, we demonstrate that approximate Bayesian computing can provide estimates
with a lower mean square error than the composite likelihood approach, though at an
appreciably higher computational cost.  We also illustrate the performance of the method
with an application to US temperature data to estimate the risk of crop loss due to an unlikely
freeze event.

This is joint with Richard Smith

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