A flexible extreme value mixture model

MacDonald, A.; Scarrott, Carl; Lee, D.; Darlow, Ben; Reale, Marco; Russell, G.

doi:10.1016/j.csda.2011.01.005

Cited by 116 publications

(79 citation statements)

References 22 publications

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“…In recent years, efforts have been made to overcome the problem of visual threshold selection, e.g., by robust threshold selection (Dupuis, 1999), likelihood-based visual diagnostics (Wadsworth and Tawn, 2012;Wadsworth, 2016), Bayesian approaches (Tancredi et al, 2006;Lee et al, 2014), approaches based on goodnessof-fit tests (Roth et al, 2016) and extreme value mixture models (MacDonald et al, 2011). In addition, attempts were made to develop more automated approaches for extreme value threshold estimation, including the automated threshold selection approach (ATSM) by Thompson et al (2009), the multiple threshold method (MTM) by Deidda (2010) and the automatic threshold and run parameter selection by Fukutome et al (2015).…”

Section: Discussionmentioning

confidence: 99%

Extreme weather exposure identification for road networks – a comparative assessment of statistical methods

Schlögl

Laaha

2017

Nat. Hazards Earth Syst. Sci.

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Abstract. The assessment of road infrastructure exposure to extreme weather events is of major importance for scientists and practitioners alike. In this study, we compare the different extreme value approaches and fitting methods with respect to their value for assessing the exposure of transport networks to extreme precipitation and temperature impacts. Based on an Austrian data set from 25 meteorological stations representing diverse meteorological conditions, we assess the added value of partial duration series (PDS) over the standardly used annual maxima series (AMS) in order to give recommendations for performing extreme value statistics of meteorological hazards. Results show the merits of the robust L-moment estimation, which yielded better results than maximum likelihood estimation in 62 % of all cases. At the same time, results question the general assumption of the threshold excess approach (employing PDS) being superior to the block maxima approach (employing AMS) due to information gain. For low return periods (non-extreme events) the PDS approach tends to overestimate return levels as compared to the AMS approach, whereas an opposite behavior was found for high return levels (extreme events). In extreme cases, an inappropriate threshold was shown to lead to considerable biases that may outperform the possible gain of information from including additional extreme events by far. This effect was visible from neither the square-root criterion nor standardly used graphical diagnosis (mean residual life plot) but rather from a direct comparison of AMS and PDS in combined quantile plots. We therefore recommend performing AMS and PDS approaches simultaneously in order to select the best-suited approach. This will make the analyses more robust, not only in cases where threshold selection and dependency introduces biases to the PDS approach but also in cases where the AMS contains non-extreme events that may introduce similar biases. For assessing the performance of extreme events we recommend the use of conditional performance measures that focus on rare events only in addition to standardly used unconditional indicators. The findings of the study directly address road and traffic management but can be transferred to a range of other environmental variables including meteorological and hydrological quantities.

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Section: Discussionmentioning

confidence: 99%

Extreme weather exposure identification for road networks – a comparative assessment of statistical methods

Schlögl

Laaha

2017

Nat. Hazards Earth Syst. Sci.

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“…Examples include the work of Frigessi et al (2002), Behrens et al (2004), MacDonald et al (2011) and Randell et al (2015). At the current time, however, given sample quality and the need for a simple "designer" distribution for straightforward application, we judge the proposed WGP model fit for purpose .…”

Section: Discussion and Suggestions For Further Investigationmentioning

confidence: 99%

On the distribution of wave height in shallow water

Randell

Christou

et al. 2016

Coastal Engineering

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The statistical distribution of the height of sea waves in deep water has been modelled using the Rayleigh (LonguetHiggins 1952) and Weibull distributions (Forristall 1978). Depth-induced wave breaking leading to restriction on the ratio of wave height to water depth require new parameterisations of these or other distributional forms for shallow water. Glukhovskiy (1966) proposed a Weibull parameterisation accommodating depth-limited breaking, modified by van Vledder (1991). Battjes and Groenendijk (2000) suggested a two-part Weibull-Weibull distribution. Here we propose a two-part Weibull-generalised Pareto model for wave height in shallow water, parameterised empirically in terms of sea state parameters (significant wave height, H S , local wave-number, k L , and water depth, d), using data from both laboratory and field measurements from 4 o↵shore locations. We are particularly concerned that the model can be applied usefully in a straightforward manner; given three pre-specified universal parameters, the model further requires values for sea state significant wave height and wave number, and water depth so that it can be applied. The model has continuous probability density, smooth cumulative distribution function, incorporates the Miche upper limit for wave heights (Miche 1944) and adopts H S as the transition wave height from Weibull body to generalised Pareto tail forms. Accordingly, the model is e↵ectively a new form for the breaking wave height distribution. The estimated model provides good predictive performance on laboratory and field data.

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“…Alternative automated threshold selection methods, such as those of Behrens et al (2004), Tancredi et al (2006), andMacDonald et al (2011), model the data below the threshold by fitting a parametric or more flexible model to the bulk of the distribution while fitting a GPD or other extreme value model above the threshold. As extremes methods wish to "let the tail speak for itself", a concern of any approach which uses non-extreme data is that the data in the bulk of the distribution could contaminate tail inference.…”

Section: Traditional Threshold Exceedance Methodsmentioning

confidence: 99%

“…Furthermore, the point process representation of the GPD can be used to overcome the scale and threshold dependence issue. The models of both Tancredi et al (2006) and MacDonald et al (2011) proceed in such a matter. Tancredi et al (2006) use a "mixture of uniforms" density estimator for f 1 , whereas MacDonald et al (2011) use a symmetric kernel density estimator for f 1 .…”

Section: Unsuccessful Attempts To Estimate U τmentioning

confidence: 99%

Modeling the upper tail of the distribution of facial recognition non-match scores

Hunter

Cooley

Givens

et al. 2017

Statistics and Its Interface

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Modeling the Upper Tail of the Distribution of Facial Recognition Non-match ScoresIn facial recognition applications, the upper tail of the distribution of non-match scores is of interest because existing algorithms classify a pair of images as a match if their score exceeds some high quantile of the non-match distribution. I construct a general model for the distribution above the (1 − τ )th quantile borrowing ideas from extreme value theory. The resulting distribution can be viewed as a reparameterized generalized Pareto distribution (GPD), but it differs from the traditional GPD in that τ is treated as fixed. Inference for both the (1 − τ )th quantile u τ and the GPD scale and shape parameters is performed via M-estimation, where my objective function is a combination of the quantile regression loss function and reparameterized GPD densities.By parameterizing u τ and the GPD parameters in terms of available covariates, understanding of these covariates' influence on the tail of the distribution of non-match scores is attained. A simulation study shows that my method is able to estimate both the set of parameters describing the covariates' influence and high quantiles of the non-match distribution. The simulation study also shows that my model is competitive with quantile regression in estimating high quantiles and that it outperforms quantile regression for extremely high quantiles. I apply my method to a data set of non-match scores and find that covariates such as gender, use of glasses, and age difference have a strong influence on the tail of the non-match distribution.ii

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A flexible extreme value mixture model

Cited by 116 publications

References 22 publications

Extreme weather exposure identification for road networks – a comparative assessment of statistical methods

Extreme weather exposure identification for road networks – a comparative assessment of statistical methods

On the distribution of wave height in shallow water

Modeling the upper tail of the distribution of facial recognition non-match scores

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