1 research outputs found
Asymptotic models and inference for extremes of spatio-temporal data
Recently there has been a lot of effort to model extremes of spatially
dependent data. These efforts seem to be divided into two distinct groups: the study of
max-stable processes, together with the development of statistical models within this
framework; the use of more pragmatic, flexible models using Bayesian hierarchical
models (BHM) and simulation based inference techniques. Each modeling strategy
has its strong and weak points. While max-stable models capture the local behavior
of spatial extremes correctly, hierarchical models based on the conditional independence
assumption, lack the asymptotic arguments the max-stable models enjoy. On
the other hand, they are very flexible in allowing the introduction of physical plausibility
into the model. When the objective of the data analysis is to estimate return
levels or kriging of extreme values in space, capturing the correct dependence structure
between the extremes is crucial and max-stable processes are better suited for
these purposes. However when the primary interest is to explain the sources of
variation in extreme events Bayesian hierarchical modeling is a very flexible tool
due to the ease with which random effects are incorporated in the model. In this
paper we model a data set on Portuguese wildfires to show the flexibility of BHM in
incorporating spatial dependencies acting at different resolutions