10,093 research outputs found
Spatial modeling of extreme snow depth
The spatial modeling of extreme snow is important for adequate risk
management in Alpine and high altitude countries. A natural approach to such
modeling is through the theory of max-stable processes, an infinite-dimensional
extension of multivariate extreme value theory. In this paper we describe the
application of such processes in modeling the spatial dependence of extreme
snow depth in Switzerland, based on data for the winters 1966--2008 at 101
stations. The models we propose rely on a climate transformation that allows us
to account for the presence of climate regions and for directional effects,
resulting from synoptic weather patterns. Estimation is performed through
pairwise likelihood inference and the models are compared using penalized
likelihood criteria. The max-stable models provide a much better fit to the
joint behavior of the extremes than do independence or full dependence models.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS464 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Model misspecification in peaks over threshold analysis
Classical peaks over threshold analysis is widely used for statistical
modeling of sample extremes, and can be supplemented by a model for the sizes
of clusters of exceedances. Under mild conditions a compound Poisson process
model allows the estimation of the marginal distribution of threshold
exceedances and of the mean cluster size, but requires the choice of a
threshold and of a run parameter, , that determines how exceedances are
declustered. We extend a class of estimators of the reciprocal mean cluster
size, known as the extremal index, establish consistency and asymptotic
normality, and use the compound Poisson process to derive misspecification
tests of model validity and of the choice of run parameter and threshold.
Simulated examples and real data on temperatures and rainfall illustrate the
ideas, both for estimating the extremal index in nonstandard situations and for
assessing the validity of extremal models.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS292 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Bayesian Inference from Composite Likelihoods, with an Application to Spatial Extremes
Composite likelihoods are increasingly used in applications where the full
likelihood is analytically unknown or computationally prohibitive. Although the
maximum composite likelihood estimator has frequentist properties akin to those
of the usual maximum likelihood estimator, Bayesian inference based on
composite likelihoods has yet to be explored. In this paper we investigate the
use of the Metropolis--Hastings algorithm to compute a pseudo-posterior
distribution based on the composite likelihood. Two methodologies for adjusting
the algorithm are presented and their performance on approximating the true
posterior distribution is investigated using simulated data sets and real data
on spatial extremes of rainfall
A statistical model for contamination due to long-range atmospheric transport of radionuclides
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Likelihood estimators for multivariate extremes
The main approach to inference for multivariate extremes consists in
approximating the joint upper tail of the observations by a parametric family
arising in the limit for extreme events. The latter may be expressed in terms
of componentwise maxima, high threshold exceedances or point processes,
yielding different but related asymptotic characterizations and estimators. The
present paper clarifies the connections between the main likelihood estimators,
and assesses their practical performance. We investigate their ability to
estimate the extremal dependence structure and to predict future extremes,
using exact calculations and simulation, in the case of the logistic model
Statistical Modeling of Spatial Extremes
The areal modeling of the extremes of a natural process such as rainfall or
temperature is important in environmental statistics; for example,
understanding extreme areal rainfall is crucial in flood protection. This
article reviews recent progress in the statistical modeling of spatial
extremes, starting with sketches of the necessary elements of extreme value
statistics and geostatistics. The main types of statistical models thus far
proposed, based on latent variables, on copulas and on spatial max-stable
processes, are described and then are compared by application to a data set on
rainfall in Switzerland. Whereas latent variable modeling allows a better fit
to marginal distributions, it fits the joint distributions of extremes poorly,
so appropriately-chosen copula or max-stable models seem essential for
successful spatial modeling of extremes.Comment: Published in at http://dx.doi.org/10.1214/11-STS376 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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