ABC model selection for spatial max-stable models applied to South Australian maximum temperature data
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Max-stable processes are a common choice for modelling spatial extreme data as they arise naturally as the infinite-dimensional generalisation of multivariate extreme value theory. Statistical inference for such models is complicated by the intractability of the multivariate density function. Nonparametric and composite likelihood-based approaches have been proposed to address this difficulty. More recently, a simulation-based approach using approximate Bayesian computation (ABC) has been employed for estimating parameters of max-stable models. ABC algorithms rely on the evaluation of discrepancies between model simulations and the observed data rather than explicit evaluations of computationally expensive or intractable likelihood functions. The use of an ABC method to perform model selection for max-stable models is explored. Four max-stable models are considered: the extremal-t model with either a Whittle-Matern, Cauchy or powered exponential covariance function, and the Brown-Resnick model. The method is applied to annual maximum temperature data from 25 weather stations dispersed around South Australia.
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