2,265 research outputs found
Local likelihood estimation of complex tail dependence structures, applied to U.S. precipitation extremes
To disentangle the complex non-stationary dependence structure of
precipitation extremes over the entire contiguous U.S., we propose a flexible
local approach based on factor copula models. Our sub-asymptotic spatial
modeling framework yields non-trivial tail dependence structures, with a
weakening dependence strength as events become more extreme, a feature commonly
observed with precipitation data but not accounted for in classical asymptotic
extreme-value models. To estimate the local extremal behavior, we fit the
proposed model in small regional neighborhoods to high threshold exceedances,
under the assumption of local stationarity, which allows us to gain in
flexibility. Adopting a local censored likelihood approach, inference is made
on a fine spatial grid, and local estimation is performed by taking advantage
of distributed computing resources and the embarrassingly parallel nature of
this estimation procedure. The local model is efficiently fitted at all grid
points, and uncertainty is measured using a block bootstrap procedure. An
extensive simulation study shows that our approach can adequately capture
complex, non-stationary dependencies, while our study of U.S. winter
precipitation data reveals interesting differences in local tail structures
over space, which has important implications on regional risk assessment of
extreme precipitation events
Point process-based modeling of multiple debris flow landslides using INLA: an application to the 2009 Messina disaster
We develop a stochastic modeling approach based on spatial point processes of
log-Gaussian Cox type for a collection of around 5000 landslide events provoked
by a precipitation trigger in Sicily, Italy. Through the embedding into a
hierarchical Bayesian estimation framework, we can use the Integrated Nested
Laplace Approximation methodology to make inference and obtain the posterior
estimates. Several mapping units are useful to partition a given study area in
landslide prediction studies. These units hierarchically subdivide the
geographic space from the highest grid-based resolution to the stronger
morphodynamic-oriented slope units. Here we integrate both mapping units into a
single hierarchical model, by treating the landslide triggering locations as a
random point pattern. This approach diverges fundamentally from the unanimously
used presence-absence structure for areal units since we focus on modeling the
expected landslide count jointly within the two mapping units. Predicting this
landslide intensity provides more detailed and complete information as compared
to the classically used susceptibility mapping approach based on relative
probabilities. To illustrate the model's versatility, we compute absolute
probability maps of landslide occurrences and check its predictive power over
space. While the landslide community typically produces spatial predictive
models for landslides only in the sense that covariates are spatially
distributed, no actual spatial dependence has been explicitly integrated so far
for landslide susceptibility. Our novel approach features a spatial latent
effect defined at the slope unit level, allowing us to assess the spatial
influence that remains unexplained by the covariates in the model
Max-infinitely divisible models and inference for spatial extremes
For many environmental processes, recent studies have shown that the
dependence strength is decreasing when quantile levels increase. This implies
that the popular max-stable models are inadequate to capture the rate of joint
tail decay, and to estimate joint extremal probabilities beyond observed
levels. We here develop a more flexible modeling framework based on the class
of max-infinitely divisible processes, which extend max-stable processes while
retaining dependence properties that are natural for maxima. We propose two
parametric constructions for max-infinitely divisible models, which relax the
max-stability property but remain close to some popular max-stable models
obtained as special cases. The first model considers maxima over a finite,
random number of independent observations, while the second model generalizes
the spectral representation of max-stable processes. Inference is performed
using a pairwise likelihood. We illustrate the benefits of our new modeling
framework on Dutch wind gust maxima calculated over different time units.
Results strongly suggest that our proposed models outperform other natural
models, such as the Student-t copula process and its max-stable limit, even for
large block sizes
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