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Person# Jonathan A. Tawn

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Related research domains (3)

Multivariate normal distribution

In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) no

Bayesian inference

Bayesian inference (ˈbeɪziən or ˈbeɪʒən ) is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes avail

Extreme value theory

Extreme value theory or extreme value analysis (EVA) is a branch of statistics dealing with the extreme deviations from the median of probability distributions. It seeks to assess, from a given ord

Related publications (6)

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Anthony Christopher Davison, Thomas Lugrin, Jonathan A. Tawn

Both marginal and dependence features must be described when modelling the extremes of a stationary time series. There are standard approaches to marginal modelling, but long- and short-range dependence of extremes may both appear. In applications, an assumption of long-range independence often seems reasonable, but short-range dependence, i.e., the clustering of extremes, needs attention. The extremal index $0

Anthony Christopher Davison, Thomas Lugrin, Jonathan A. Tawn

Statistical models for extreme values are generally derived from non-degenerate probabilistic limits that can be used to approximate the distribution of events that exceed a selected high threshold. If convergence to the limit distribution is slow, then the approximation may describe observed extremes poorly, and bias can only be reduced by choosing a very high threshold at the cost of unacceptably large variance in any subsequent tail inference. An alternative is to use sub-asymptotic extremal models, which introduce more parameters but can provide better fits for lower thresholds. We consider this problem in the context of the Heffernan–Tawn conditional tail model for multivariate extremes, which has found wide use due to its flexible handling of dependence in high-dimensional applications. Recent extensions of this model appear to improve joint tail inference. We seek a sub-asymptotic justification for why these extensions work and show that they can improve convergence rates by an order of magnitude for certain copulas. We also propose a class of extensions of them that may have wider value for statistical inference in multivariate extremes.

2021Anthony Christopher Davison, Jonathan A. Tawn, Jennifer Lynne Wadsworth

Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent. Most available statistical models suit one or other of these cases, but not both, resulting in a stage in the inference that is unaccounted for but can substantially impact subsequent extrapolation. Existing modelling solutions to this problem are either applicable only on subdomains or appeal to multiple limit theories. We introduce a unified representation for bivariate extremes that encompasses a wide variety of dependence scenarios and applies when at least one variable is large. Our representation motivates a parametric model that encompasses both dependence classes. We implement a simple version of this model and show that it performs well in a range of settings.