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  • Faculty of Design and Creative Technologies (Te Ara Auaha)
  • School of Engineering, Computer and Mathematical Sciences - Te Kura Mātai Pūhanga, Rorohiko, Pāngarau
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Bayesian threshold selection for extremal models using measures of surprise

Lee, J; Fan, Y; Sisson, S
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http://hdl.handle.net/10292/8220
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Abstract
Statistical extreme value theory is concerned with the use of asymptotically motivated models to describe the extreme values of a process. A number of commonly used models are valid for observed data that exceed some high threshold. However, in practice a suitable threshold is unknown and must be determined for each analysis.

While there are many threshold selection methods for univariate extremes, there are relatively few that can be applied in the multivariate setting. In addition, there are only a few Bayesian-based methods, which are naturally attractive in the modelling of extremes due to data scarcity. The use of Bayesian measures of surprise to determine suitable thresholds for extreme value models is proposed. Such measures quantify the level of support for the proposed extremal model and threshold, without the need to specify any model alternatives. This approach is easily implemented for both univariate and multivariate extremes.
Keywords
Bayesian inference; Extremes; Generalized Pareto distribution; Posterior predictive p-value; Spectral density function; Surprise; Threshold selection
Date
November 14, 2013
Source
arXiv. arXiv:1311.2994v2 [stat.ME]
Item Type
Journal Article
Publisher
Cornell University Library
Publisher's Version
http://arxiv.org/abs/1311.2994
Rights Statement
arXiv supports and participates in the Open Archives Initiative (OAI). arXiv is a registered OAI-PMH data-provider and provides metadata for all submissions which is updated each night shortly after new submissions are announced. Metadata for arXiv articles may be reused in non-commercial and commercial systems.

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