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Host: Institute for Mathematics and its Applications
Homepage: http://www.ima.umn.edu/geoscience/spring/g11.html
Email: staff@ima.umn.edu
Organizers: Frederick Schoenberg, David R. Brillinger, Bruce Bolt
Description:
The daily topics will include the following.
1) Introduction to earthquakes. This topic will motivate the workshop. Seismic hazard estimation will be examined as a paradigm of a problem in the Earth Sciences for which there already is a repertoire of statistical methodology and substantial room for improvement in the use of statistics.
2) The role of `randomness' in seismology. While seismologists traditionally describe earthquakes via deterministic, physical models, applied statisticians have increasingly explored the use of stochastic, or "random" models for earthquake behavior. It is important to explore questions such as: Which characteristics of earthquakes may usefully described as "random"? What roles can stochastic point process or time series models play in addressing useful seismological problems? In particular, questions of scale come into play, as deterministic models may be useful in describing phenomena which, on a relatively macroscopic scale, appear to behave randomly, and vice versa.
3) Time series versus point processes. The main stochastic models used for describing earthquakes come from the areas of time series and point processes. Time series models are generally used in describing random processes that appear to be sampled at discrete time points. Point processes are useful for modeling random processes that appear at irregularly spaced times, and which may conceivably occur anywhere in a continuum of possible times. Rather little attention has been given to how these two classes of models compare, and in which applications to use one type of model as opposed to the other. These questions will motivate an introduction and discussion of the two types of models in a context that will be both useful and accessible to seismologists and other earth scientists. In addition, special attention will focus on conditional rate (or conditional intensity) models for point process, which have proven useful in describing earthquake occurrences but whose descriptions are rather intricate.
4) Statistical models for seismological processes. Seismologists have predominantly explored physical models in describing earthquakes. Such models are generally deterministic descriptions of physical phenomena and how they interact within a closed and well-defined environment, and typically are expressed as differential equations, ordinary or partial (e.g. Newton's laws of motion). By contrast, statistical models are often used to describe observations of phenomena which are thought to have some inherent variability or which are observed with incomplete information, such as data recorded with error or events occurring at an irregular and uncertain pattern of locations and times. (Sometimes the statistical model incorporates the mathematical solution to a physical model, but in many situations this is not entirely possible.) Statistical models may be especially useful in quantifying uncertainties related to previously observed phenomena as well as to forecasts of future events. We will explore examples of these models in detail, and discuss how they may be used to address basic seismological problems of concern. Of particular interest are point process models including stress-release processes and other state-space models, branching processes, renewal processes, and mixture models. Special attention will be paid to issues involving spatial-temporal marked point processes and their applications to seismological data.
5) Evaluation of statistical models. Many different statistical models can and indeed have frequently been used to describe the same seismological phenomena. Thus, given a statistical model, a very important and basic question is: how adequately does the model describe the data (observations or simulations) to which it applies, and how does the fit of the model in question compare to competing statistical models? We will survey methods, both graphical and numerical, for assessing goodness-of-fit for stochastic models for seismological processes. Further, we will discuss practical implications, including which types of models appear to fit well to which seismic datasets, and what can be deduced in terms of construction of confidence intervals, standard errors, and statistical tests.
Keywords: Risk assessment, seismic hazard estimation, prediction, point process (theory and applications), marked point process, earthquakes, insurance
Date received: January 31, 2001
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