129 research outputs found
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
Bayesian uncertainty management in temporal dependence of extremes
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 < ≤ 1 is a natural limiting measure of clustering, but for wide classes of dependent processes, including all stationary Gaussian processes, it cannot distinguish dependent processes from independent processes with = 1. Eastoe and Tawn (Biometrika 99, 43–55 2012) exploit methods from multivariate extremes to treat the subasymptotic extremal dependence structure of stationary time series, covering both 0 < <1 and = 1, through the introduction of a threshold-based extremal index. Inference for their dependence models uses an inefficient stepwise procedure that has various weaknesses and has no reliable assessment of uncertainty. We overcome these issues using a Bayesian semiparametric approach. Simulations and the analysis of a UK daily river flow time series show that the new approach provides improved efficiency for estimating properties of functionals of clusters
The SKA Particle Array Prototype: The First Particle Detector at the Murchison Radio-astronomy Observatory
We report on the design, deployment, and first results from a scintillation
detector deployed at the Murchison Radio-astronomy Observatory (MRO). The
detector is a prototype for a larger array -- the Square Kilometre Array
Particle Array (SKAPA) -- planned to allow the radio-detection of cosmic rays
with the Murchison Widefield Array and the low-frequency component of the
Square Kilometre Array. The prototype design has been driven by stringent
limits on radio emissions at the MRO, and to ensure survivability in a desert
environment. Using data taken from Nov.\ 2018 to Feb.\ 2019, we characterize
the detector response while accounting for the effects of temperature
fluctuations, and calibrate the sensitivity of the prototype detector to
through-going muons. This verifies the feasibility of cosmic ray detection at
the MRO. We then estimate the required parameters of a planned array of eight
such detectors to be used to trigger radio observations by the Murchison
Widefield Array.Comment: 17 pages, 14 figures, 3 table
Intermediate Tail Dependence: A Review and Some New Results
The concept of intermediate tail dependence is useful if one wants to
quantify the degree of positive dependence in the tails when there is no strong
evidence of presence of the usual tail dependence. We first review existing
studies on intermediate tail dependence, and then we report new results to
supplement the review. Intermediate tail dependence for elliptical, extreme
value and Archimedean copulas are reviewed and further studied, respectively.
For Archimedean copulas, we not only consider the frailty model but also the
recently studied scale mixture model; for the latter, conditions leading to
upper intermediate tail dependence are presented, and it provides a useful way
to simulate copulas with desirable intermediate tail dependence structures.Comment: 25 pages, 1 figur
Extreme events of Markov chains
The extremal behaviour of a Markov chain is typically characterized by its
tail chain. For asymptotically dependent Markov chains existing formulations
fail to capture the full evolution of the extreme event when the chain moves
out of the extreme tail region and for asymptotically independent chains recent
results fail to cover well-known asymptotically independent processes such as
Markov processes with a Gaussian copula between consecutive values. We use more
sophisticated limiting mechanisms that cover a broader class of asymptotically
independent processes than current methods, including an extension of the
canonical Heffernan-Tawn normalization scheme, and reveal features which
existing methods reduce to a degenerate form associated with non-extreme
states.Comment: 29 pages, 2 figure
Tide and skew surge independence: new insights for flood risk
Storm surges are a significant hazard to coastal communities around the world, putting lives at risk and costing billions of dollars in damage. Understanding how storm surges and high tides interact is crucial for estimating extreme water levels so that we can protect coastal communities. We demonstrate that in a tidal regime the best measure of a storm surge is the skew surge, the difference between the observed and predicted high water within a tidal cycle.
Based on tide gauge records spanning decades from the UK, US, Netherlands and Ireland we show that the magnitude of high water exerts no influence on the size of the most extreme skew surges. This is the first systematic proof that any storm surge can occur on any tide, which is essential for understanding worst case scenarios. The lack of surge generation dependency on water depth emphasises the dominant natural variability of weather systems in an observations-based analysis. Weak seasonal relationships between skew surges and high waters were identified at a minority of locations where long period changes to the tidal cycle interact with the storm season. Our results allow advances to be made in methods for estimating the joint probabilities of storm surges and tides
On the study of extremes with dependent random right-censoring
The study of extremes in missing data frameworks is a recent developing field. In particular, the randomly right-censored case has been receiving a fair amount of attention in the last decade. All studies on this topic, however, essentially work under the usual assumption that the variable of interest and the censoring variable are independent. Furthermore, a frequent characteristic of estimation procedures developed so far is their crucial reliance on particular properties of the asymptotic behaviour of the response variable Z (that is, the minimum between time-to-event and time-to-censoring) and of the probability of censoring in the right tail of Z. In this paper, we focus instead on elucidating this asymptotic behaviour in the dependent censoring case, and, more precisely, when the structure of the dependent censoring mechanism is given by an extreme value copula. We then draw a number of consequences of our results, related to the asymptotic behaviour, in this dependent context, of a number of estimators of the extreme value index of the random variable of interest that were introduced in the literature under the assumption of independent censoring, and we discuss more generally the implications of our results on the inference of the extremes of this variable
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