On the occurrence times of componentwise maxima and bias in likelihood inference for multivariate max-stable distributions

Full likelihood-based inference for high-dimensional multivariate extreme value distributions, or max-stable processes, is feasible when incorporating occurrence times of the maxima; without this information, $d$-dimensional likelihood inference is usually precluded due to the large number of terms in the likelihood. However, some studies have noted bias when performing high-dimensional inference that incorporates such event information, particularly when dependence is weak. We elucidate this phenomenon, showing that for unbiased inference in moderate dimensions, dimension $d$ should be of a magnitude smaller than the square root of the number of vectors over which one takes the componentwise maximum. A bias reduction technique is suggested and illustrated on the extreme value logistic model.Comment: 7 page

Failure environment analysis tool applications

Understanding risks and avoiding failure are daily concerns for the women and men of NASA. Although NASA's mission propels us to push the limits of technology, and though the risks are considerable, the NASA community has instilled within, the determination to preserve the integrity of the systems upon which our mission and, our employees lives and well-being depend. One of the ways this is being done is by expanding and improving the tools used to perform risk assessment. The Failure Environment Analysis Tool (FEAT) was developed to help engineers and analysts more thoroughly and reliably conduct risk assessment and failure analysis. FEAT accomplishes this by providing answers to questions regarding what might have caused a particular failure; or, conversely, what effect the occurrence of a failure might have on an entire system. Additionally, FEAT can determine what common causes could have resulted in other combinations of failures. FEAT will even help determine the vulnerability of a system to failures, in light of reduced capability. FEAT also is useful in training personnel who must develop an understanding of particular systems. FEAT facilitates training on system behavior, by providing an automated environment in which to conduct 'what-if' evaluation. These types of analyses make FEAT a valuable tool for engineers and operations personnel in the design, analysis, and operation of NASA space systems

Accounting for choice of measurement scale in extreme value modeling

We investigate the effect that the choice of measurement scale has upon inference and extrapolation in extreme value analysis. Separate analyses of variables from a single process on scales which are linked by a nonlinear transformation may lead to discrepant conclusions concerning the tail behavior of the process. We propose the use of a Box--Cox power transformation incorporated as part of the inference procedure to account parametrically for the uncertainty surrounding the scale of extrapolation. This has the additional feature of increasing the rate of convergence of the distribution tails to an extreme value form in certain cases and thus reducing bias in the model estimation. Inference without reparameterization is practicably infeasible, so we explore a reparameterization which exploits the asymptotic theory of normalizing constants required for nondegenerate limit distributions. Inference is carried out in a Bayesian setting, an advantage of this being the availability of posterior predictive return levels. The methodology is illustrated on both simulated data and significant wave height data from the North Sea.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS333 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Determining the Dependence Structure of Multivariate Extremes

In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies with determining which subsets of variables can take their largest values simultaneously, while the others are of smaller order. Our approach to this problem exploits hidden regular variation properties on a collection of non-standard cones and provides a new set of indices that reveal aspects of the extremal dependence structure not available through existing measures of dependence. We derive theoretical properties of these indices, demonstrate their value through a series of examples, and develop methods of inference that also estimate the proportion of extremal mass associated with each cone. We apply the methods to UK river flows, estimating the probabilities of different subsets of sites being large simultaneously

The Role of Worker Flows in the Dynamics and Distribution of UK Unemployment

Unemployment varies substantially over time and across subgroups of the labour market. Worker flows among labour market states act as key determinants of this variation. We examine how the structure of unemployment across groups and its cyclical movements across time are shaped by changes in labour market flows. Using novel estimates of flow transition rates for the UK over the last 35 years, we decompose unemployment variation into parts accounted for by changes in rates of job loss, job finding and flows via non-participation. Close to two-thirds of the volatility of unemployment in the UK over this period can be traced to rises in rates of job loss that accompany recessions. The share of this inflow contribution has been broadly the same in each of the past three recessions. Decreased jobfinding rates account for around one-quarter of unemployment cyclicality and the remaining variation can be attributed to flows via non-participation. Digging deeper into the structure of unemployment by gender, age and education, the flow-approach is shown to provide a richer understanding of the unemployment experiences across population subgroups.labour market, unemployment, worker flows

Higher-dimensional spatial extremes via single-site conditioning

Currently available models for spatial extremes suffer either from inflexibility in the dependence structures that they can capture, lack of scalability to high dimensions, or in most cases, both of these. We present an approach to spatial extreme value theory based on the conditional multivariate extreme value model, whereby the limit theory is formed through conditioning upon the value at a particular site being extreme. The ensuing methodology allows for a flexible class of dependence structures, as well as models that can be fitted in high dimensions. To overcome issues of conditioning on a single site, we suggest a joint inference scheme based on all observation locations, and implement an importance sampling algorithm to provide spatial realizations and estimates of quantities conditioning upon the process being extreme at any of one of an arbitrary set of locations. The modelling approach is applied to Australian summer temperature extremes, permitting assessment the spatial extent of high temperature events over the continent

LXIV. Description of a very sensitive form of Thomson galvanometer, and some methods of galvanometer construction

n/

Efficient inference for spatial extreme value processes associated to log-Gaussian random functions

Max-stable processes arise as the only possible nontrivial limits for maxima of affinely normalized identically distributed stochastic processes, and thus form an important class of models for the extreme values of spatial processes. Until recently, inference for max-stable processes has been restricted to the use of pairwise composite likelihoods, due to intractability of higher-dimensional distributions. In this work we consider random fields that are in the domain of attraction of a widely used class of max-stable processes, namely those constructed via manipulation of log-Gaussian random functions. For this class, we exploit limiting d-dimensional multivariate Poisson process intensities of the underlying process for inference on all d-vectors exceeding a high marginal threshold in at least one component, employing a censoring scheme to incorporate information below the marginal threshold. We also consider the d-dimensional distributions for the equivalent max-stable process, and perform full likelihood inference by exploiting the methods of Stephenson & Tawn (2005), where information on the occurrence times of extreme events is shown to dramatically simplify the likelihood. The Stephenson-Tawn likelihood is in fact simply a special case of the censored Poisson process likelihood. We assess the improvements in inference from both methods over pairwise likelihood methodology by simulatio