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

A review of very short-term wind and solar power forecasting

Installed capacities of wind and solar power have grown rapidly over recent years, and the pool of literature on very short-term (minutes- to hours-ahead) wind and solar forecasting has grown in line with this. This paper reviews established and emerging approaches to provide an up-to-date view of the field. Knowledge transfer between wind and solar forecasting has benefited the field and is discussed, and new opportunities are identified, particularly regarding use of remote sensing technology. Forecasting methodologies and study design are compared and recommendations for high quality, reproducible results are presented. In particular, the choice of suitable benchmarks and use of sufficiently long datasets is highlighted. A case study of three distinct approaches to probabilistic wind power forecasting is presented using an open dataset. The case study provides an example of exemplary forecast evaluation, and open source code allows for its reproduction and use in future work

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

Chromosome aberrations in lymphocytes of workers occupationally exposed to ionising radiation

Cytogenetic studies on workers employed at the Sellafield nuclear installation are reviewed and their relevance discussed in relation to biological dosimetry and risk assessment

Analyzing monthly extreme sea levels with a time-dependent GEV model

A statistical model to analyze different time scales of the variability of extreme high sea levels is presented. This model uses a time-dependent generalized extreme value (GEV) distribution to fit monthly maxima series and is applied to a large historical tidal gauge record (San Francisco, California). The model allows the identification and estimation of the effects of several time scales —such as seasonality, interdecadal variability, and secular trends— in the location, scale, and shape parameters of the probability distribution of extreme sea levels. The inclusion of seasonal effects explains a large amount of data variability, thereby allowing a more efficient estimation of the processes involved. Significant correlation with the Southern Oscillation index and the nodal cycle, as well as an increase of about 20% for the secular variability of the scale parameter have been detected for the particular dataset analyzed. Results show that the model is adequate for a complete analysis of seasonal-to-interannual sea level extremes providing time-dependent quantiles and confidence intervals

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