Annual Report 2008.pdf - SAMSI

Large pyroclastic flows are rare yet potentially devastating events for communities situated near
volcanoes. We propose a method to draw hazard maps that combines field data, digital elevation
maps, and flow simulations. As a test case, we focus on calculating probabilities of catastrophic
damage due to flow events from the Soufriere Hills Volcano on the island of Montserrat.
Jery Stedinger
Cornell University
jrs5@cornell.edu
“Regionalization of Statistics Describing the Distribution of Hydrologic Extremes”
The three-parameter Generalized Extreme Value (GEV) distribution is widely used to describe
annual floods, rainfall, wind speeds, and other maxima. Studies showed that small-sample at-site
MLE GEV parameter estimators are unstable, and recommend L-moment estimators. Use of a
Bayesian prior to restrict shape-parameter-values to a statistically-physically reasonable range
yields Generalized Maximum Likelihood (GML) estimators. GML estimators eliminate
problems with MLEs and perform substantially better than both moment and L-moment quantile
estimators for heavy-tailed GEV distributions. Of great interest are data-based priors for shape
parameters. We have developed a Bayesian Generalized Least Squares (B-GLS) regression
methodology that accounts for the sampling error in at-site estimators due to finite-length
records, the cross-correlation among such estimators due to the cross-correlation among
concurrent annual maxima, and the actual precision of the underlying model. B-GLS provides a
statistically efficient and practical regionalization methodology with a range of useful diagnostic
statistics. Examples illustrate development of regional GEV shape parameters.
Stilian Stoev
University of Michigan
sstoev@umich.edu
“Max-Stable Processes: Representations, Ergodic Properties and Statistical Applications”
Max-stable stochastic processes arise in the limit of component-wise maxima of independent
processes, under appropriate centering and normalization. In this talk, various representations of
max-stable processes will be discussed. Then, in terms of these "spectral" representations,
necessary and sufficient conditions for the ergodicity and mixing of stationary max-stable
processes will be presented.
The large classes of moving maxima and maxima of moving maxima processes are shown to be
mixing. Other examples of ergodic doubly Stochastic processes and non-ergodic processes will
be given. The developed ergodicity and mixing conditions involve a certain measure of
dependence. We will address the statistical problem of estimating this measure of dependence.
Bas Werker
Tilburg University
Werker@TilburgUniversity.nl