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Abstract:
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Max-stable processes has been very helpful in capturing the joint spatial properties of extremes in addition to their marginal variation. However, when modeling environmental processes, it mistakenly identifies the vanishing spatial dependence as genuine asymptotic dependence. Also, weakening dependence does not necessarily imply asymptotic independence, therefore well-known models like the inverted max-stable process will not do well in inferring the asymptotic properties. In our work, we present a class of spatial processes which can be described by a small number of parameters and encompass both asymptotic dependence classes. Additionally, we add a measurement error to the established model to capture any possible random effects. The model is data-driven to transit smoothly between asymptotic dependence and independence. Inference is feasible in relatively large dimensions using adaptive metropolis algorithm. The model is applied to real-life data sets that exhibit decaying dependence structure.
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