Let *T*_{i}:=[*X*_{i}|**X**∈*∂**L*(*α*)], for *i* = 1,…,*d*, where **X** = (*X*_{1},…,*X*_{d}) is a risk vector and *∂**L*(*α*) is the associated multivariate critical layer at level *α*∈(0,1). The aim of this work is to propose a non-parametric extreme estimation procedure for the (1 − *p*_{n})-quantile of *T*_{i} for a fixed *α* and when *p*_{n}0, as the sample size *n*+*∞*. An extrapolation method is developed under the Archimedean copula assumption for the dependence structure of **X** and the von Mises condition for marginal *X*_{i}. The main result is the central limit theorem for our estimator for *p* = *p*_{n}0, when *n* tends towards infinity. A set of simulations illustrates the finite-sample performance of the proposed estimator. We finally illustrate how the proposed estimation procedure can help in the evaluation of extreme multivariate hydrological risks. Copyright © 2016 John Wiley & Sons, Ltd.

More than 90*%* of the sulfur dioxide in the air comes from human sources. Because of the adverse health effects of high levels of sulfur dioxide, specific regulations have been adopted to manage and reduce the amount of sulfur dioxide produced. However, some SO_{2} emission incidents (i.e. emission exceeding the limits established by law) still occur. The aim of this paper is to predict time series of SO_{2} concentrations in order to estimate in advance high emission episodes and analyse the influence of previous series in the prediction. Previous studies aimed to forecast SO_{2} pollution incidents are based on estimating mean values. Instead, we propose the use of quantile curves obtained from additive models as they provide not only the mean but also the whole distribution of the pollution levels. A backfitting algorithm with local polynomial kernel smoothers was used to estimate the model, and critical values of the hypothesis test were obtained by means of bootstrapping. The performance of the method was evaluated using simulated data as well as real data drawn from an SO_{2} time series of a coal-fired power station located in northern Spain. Copyright © 2016 John Wiley & Sons, Ltd.

The statistician often needs to test whether or not a time series has a seasonal first moment. The problem often arises in environmental series, where most time-ordered data display some type of periodic structure. This paper reviews the problem, proposing new statistics in both the time and frequency domains. Our new time domain statistic has an analysis of variance form that is based on the one-step-ahead prediction errors of the series. This statistic inherits the classic traits of the *F*-distribution arising in one-way analysis of variance tests, is easy to use, and is asymptotically equivalent to the likelihood ratio test. The statistics asymptotic distribution is quantified when time series parameters are estimated. In the frequency domain, a statistic modifying Fisher's classical test for a sinusoidal mean superimposed on independent and identically distributed Gaussian noise is devised. The performance and comparison of these statistics are studied via simulation. Implementation of the methods merely requires sample means, autocovariances, and periodograms of the series. Application to a data set of monthly temperatures from Tuscaloosa, Alabama, is given. Copyright © 2016 John Wiley & Sons, Ltd.

A Horvitz–Thompson-type estimator is introduced to estimate total abundance of the Bering–Chukchi–Beaufort Seas population of bowhead whales using combined visual and acoustic location data. The estimator divides sightings counts by three correction factors that are themselves estimated from various portions of the data. The first correction models how detection probabilities depend on covariates like offshore distance and visibility. The second correction adjusts for availability using the acoustic location data to estimate a time-varying smooth function of the probability that animals pass within visual range of the observation stations. The third correction accounts for whales passing during periods when one or both sighting stations were temporarily closed down. We derive an asymptotically unbiased estimator of abundance incorporating all these components and a corresponding variance estimate. Correcting the count of 4011 observed whales yields a 2011 abundance estimate of 16,820 with a 95% confidence interval of (15,176, 18,643) and an estimated annual rate of population increase of 3.7% (2.9%, 4.6%). These results are indicative of very low conservation risk for this population under the current low levels of aboriginal hunting permitted by the International Whaling Commission. Although few other capture–recapture surveys will confront exactly the same set of challenges addressed here, many studies face one or more issues that could be resolved by adapting portions of our approach or relevant underlying concepts thereof. Moreover, the generic estimator we derive represents an improved way to handle random correction factors rather than assuming fixed values. Copyright © 2016 John Wiley & Sons, Ltd.

]]>Ensemble model output statistics (EMOS) is a statistical tool for post-processing forecast ensembles of weather variables obtained from multiple runs of numerical weather prediction models in order to produce calibrated predictive probability density functions. The EMOS predictive probability density function is given by a parametric distribution with parameters depending on the ensemble forecasts. We propose an EMOS model for calibrating wind speed forecasts based on weighted mixtures of truncated normal (TN) and log-normal (LN) distributions where model parameters and component weights are estimated by optimizing the values of proper scoring rules over a rolling training period. The new model is tested on wind speed forecasts of the 50 member European Centre for Medium-range Weather Forecasts ensemble, the 11 member Aire Limitée Adaptation dynamique Développement International-Hungary Ensemble Prediction System ensemble of the Hungarian Meteorological Service, and the eight-member University of Washington mesoscale ensemble, and its predictive performance is compared with that of various benchmark EMOS models based on single parametric families and combinations thereof. The results indicate improved calibration of probabilistic and accuracy of point forecasts in comparison with the raw ensemble and climatological forecasts. The mixture EMOS model significantly outperforms the TN and LN EMOS methods; moreover, it provides better calibrated forecasts than the TN–LN combination model and offers an increased flexibility while avoiding covariate selection problems. © 2016 The Authors Environmetrics Published by JohnWiley & Sons Ltd.

]]>The on-line monitoring of water quality is of crucial interest. Control charts are well suited to perform this monitoring. However, these statistical methods need to be adapted to the particularity of the environmental data studies. In this paper, new control charts are developed to treat the case of a French river for which the parameter of interest, the Dissolved Oxygen Concentration (DOC), is characterized by a non-stationary and seasonal time evolution. The principle is to construct a test statistic, not directly based on the variable of interest, but rather on its seasonal regularity when the system is under control. The methods are studied through numerical simulation and is applied on real data. The ability of the control chart to be used as a classifier in a retrospective way is also studied. Copyright © 2016 John Wiley & Sons, Ltd.

]]>Since their introduction in 1990, regional climate models (RCMs) have been widely used to study the impact of climate change on human health, ecology, and epidemiology. To ensure that the conclusions of impact studies are well founded, it is necessary to assess the uncertainty in RCMs. This is not an easy task because two major sources of uncertainties can undermine an RCM: uncertainty in the boundary conditions needed to initialize the model and uncertainty in the model itself. Using climate data for Southern Sweden over 45 years, in this paper, we present a statistical modeling framework to assess an RCM driven by analyses. More specifically, our scientific interest here is determining whether there exist time periods during which the RCM in consideration displays the same type of spatial discrepancies from the observations. The proposed model can be seen as an exploratory tool for atmospheric modelers to identify time periods that require a further in-depth examination. Focusing on seasonal average temperature, our model relates the corresponding observed seasonal fields to the RCM output via a hierarchical Bayesian statistical model that includes a spatio-temporal calibration term. The latter, which represents the spatial error of the RCM, is in turn provided with a Dirichlet process prior, enabling clustering of the errors in time. We apply our modeling framework to data from Southern Sweden spanning the period 1 December 1962 to 30 November 2007, revealing intriguing tendencies with respect to the RCM spatial errors of seasonal average temperature. Copyright © 2016 John Wiley & Sons, Ltd.

]]>Adaptive cluster sampling is a design specifically developed for rare and clustered populations. Using this sampling design, we consider the case when an auxiliary variable is available in addition to the variable of interest. The use of auxiliary information has been shown to improve the efficiency of estimators although this results in asymptotically design-unbiased estimators. Consider wildlife population in a protected area. Its distribution and abundance can partly be influenced by such factors as disease and pollution where the presence of wildlife diseases or higher environmental pollution decreases population totals and the distribution of wildlife. This paper proposes two product estimators and their associated variance estimators for the adaptive cluster sampling design to be used when the study and auxiliary variables are negatively correlated. The exact expression of the bias together with the mean square error to the first degree of approximation has been obtained. We derived the conditions under which the proposed estimators provided a more accurate estimation than the Horvitz–Thompson and Hansen–Hurwitz estimators with adaptive cluster sampling and the product estimator with simple random sampling. A simulation study was carried out to show the performance of the proposed estimators. Moreover, theoretical findings were supported by a numerical example using real data. Copyright © 2016 John Wiley & Sons, Ltd.

]]>This paper deals with inference on extremes of heavy-tailed distributions. We assume distribution functions *F* of Pareto-type, where the right-tail behavior of *F* is characterized by a strictly positive parameter *γ*, the so-called extreme value index (EVI). In some applications, observations from closely related variables are available, with possibly identical EVI *γ*. If these variables are observed for the same time period, a procedure called BEAR estimator has recently been proposed. We modify this approach allowing for different observation periods and pairwise extreme value dependence of the variables. In addition, we present a new test for equality of the EVI. As an application, we discuss regional flood frequency analysis, where we want to combine rather short sequences of univariate observations with very different lengths measured at many gauges for joint inference. We illustrate our findings on peak discharges from 18 river gauges located at the Mulde basin in Germany, which is known for its severe summer floods, and identify relevant heterogeneous tail behavior, which is not detected by other popular methods. Copyright © 2015 John Wiley & Sons, Ltd.

We investigate an algorithm for maximum likelihood estimation of spatial generalized linear mixed models based on the Laplace approximation. We compare our algorithm with a set of alternative approaches for two datasets from the literature. The *Rhizoctonia root rot* and the *Rongelap* are, respectively, examples of binomial and count datasets modeled by spatial generalized linear mixed models. Our results show that the Laplace approximation provides similar estimates to Markov Chain Monte Carlo likelihood, Monte Carlo expectation maximization, and modified Laplace approximation. Some advantages of Laplace approximation include the computation of the maximized log-likelihood value, which can be used for model selection and tests, and the possibility to obtain realistic confidence intervals for model parameters based on profile likelihoods. The Laplace approximation also avoids the tuning of algorithms and convergence analysis, commonly required by simulation-based methods. Copyright © 2015 John Wiley & Sons, Ltd.

Analog forecasting has been applied in a variety of fields for predicting future states of complex nonlinear systems that require flexible forecasting methods. Past analog methods have almost exclusively been used in an empirical framework without the structure of a model-based approach. We propose a Bayesian model framework for analog forecasting, building upon previous analog methods but accounting for parameter uncertainty. Thus, unlike traditional analog forecasting methods, the use of Bayesian modeling allows one to rigorously quantify uncertainty to obtain realistic posterior predictive distributions. The model is applied to the long-lead time forecasting of mid-May averaged soil moisture anomalies in Iowa over a high-resolution grid of spatial locations. Sea surface temperature is used to find past time periods with similar trajectories to the current pre-forecast period. The analog model is developed on projection coefficients from a basis expansion of the soil moisture and sea surface temperature fields. Separate models are constructed for locations falling in each Iowa Crop Reporting District, and the forecasting ability of the proposed model is compared against a variety of alternative methods and metrics. Copyright © 2015 John Wiley & Sons, Ltd.

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]]>Identifying regions having large or unusual response in a spatial domain is frequently of interest in environmental and public health contexts. These regions having a large response are frequently called exceedance sets, exceedance regions, or excursion sets. We propose Bayesian methodology for constructing credible regions that either contain the exceedance sets or are contained within the exceedance sets with a specified level probability. The algorithms are simple to implement and use samples from the joint posterior predictive distribution of the process of interest. The R package ExceedanceTools implements the proposed methodology. We study the coverage properties of the methodology and also show that it has good coverage properties in practice. Simulation experiments demonstrate that the proposed method has good performance with respect to the empirical coverage and power. We apply this methodology to identify regions of high zinc concentration using soil samples collected in southwestern Wyoming. Copyright © 2015 John Wiley & Sons, Ltd.

]]>A novel clustering method for bivariate functional data is proposed to group streams based on their water–air temperature relationship. A distance measure is developed for bivariate curves by using a time-varying coefficient model and a weighting scheme. This distance is also adjusted by spatial correlation of streams via the variogram. Therefore, the proposed distance not only measures the difference among the streams with respect to their water–air temperature relationship but also accounts for spatial correlation among the streams. The proposed clustering method is applied to 62 streams in Southeast US that have paired air–water temperature measured over a ten-month period. The results show that streams in the same cluster reflect common characteristics such as solar radiation, percent forest and elevation. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In this article a Bayesian hierarchical model (BHM) for observed monthly precipitation is proposed. This BHM incorporates covariates based on an output on a fine grid from a regional meteorological model. At the data level of the BHM, the observed monthly precipitation is transformed using the Box–Cox transformation, and each month is modeled separately. To capture spatial correlation at the data level, a Gaussian field with Matérn correlation function is used. It is assumed that the data are subject to measurement error. The location and log-scale parameters at the latent level are also modeled with Gaussian fields with Matérn correlation functions. An output from a regional meteorological model on a fine grid is used to construct spatial covariates for the latent parameters of the BHM for each month of the year. These covariates are then projected onto each of the observed sites for each month and incorporated into the BHM. Markov chain Monte Carlo simulation is used for posterior inference and Bayesian kriging is used to predict the latent parameters on the grid. This BHM was applied to observed data on monthly precipitation, which come from forty sites across Iceland from the years 1958 to 2006. The data were corrected for wind, wetting, and evaporation loss. An output from a linear model of orographic precipitation defined on a 1 km by 1 km grid over Iceland was used to construct the covariates for the BHM. Copyright © 2015 John Wiley & Sons, Ltd.

]]>Reconstruction of pre-instrumental, late Holocene climate is important for understanding how climate has changed in the past and how climate might change in the future. Statistical prediction of paleoclimate from tree ring widths is challenging because tree ring widths are a one-dimensional summary of annual growth that represents a multi-dimensional set of climatic and biotic influences. We develop a Bayesian hierarchical framework using a nonlinear, biologically motivated tree ring growth model to jointly reconstruct temperature and precipitation in the Hudson Valley, New York. Using a common growth function to describe the response of a tree to climate, we allow for species-specific parameterizations of the growth response. To enable predictive backcasts, we model the climate variables with a vector autoregressive process on an annual timescale coupled with a multivariate conditional autoregressive process that accounts for temporal correlation and cross-correlation between temperature and precipitation on a monthly scale. Our multi-scale temporal model allows for flexibility in the climate response through time at different temporal scales and predicts reasonable climate scenarios given tree ring width data. Copyright © 2015 John Wiley & Sons, Ltd.

]]>This paper applies time series modeling methods to paleoclimate series for temperature, ice volume, and atmospheric concentrations of CO_{2} and CH_{4}. These series, inferred from Antarctic ice and ocean cores, are well known to move together in the transitions between glacial and interglacial periods, but the dynamic relationship between the series is open to question. A further unresolved issue is the role of Milankovitch theory, in which the glacial/interglacial cycles are correlated with orbital variations. We perform tests for Granger causality in the context of a vector autoregression model. Previous work with climate series has assumed nonstationarity and adopted a cointegration approach, but in a range of tests, we find no evidence of integrated behavior. We use conventional autoregressive methodology while allowing for conditional heteroscedasticity in the residuals, associated with the transitional periods. Copyright © 2015 John Wiley & Sons, Ltd.