Marc G. Genton

Skew-elliptical distributions and their applications : a journey beyond normality

This book reviews the state-of-the-art advances in skew-elliptical distributions and provides many new developments in a single volume, collecting theoretical results and applications previously scattered throughout the literature. The main goal of this research area is to develop flexible parametric classes of distributions beyond the classical normal distribution. The book is divided into two parts. The first part discusses theory and inference for skew-elliptical distribution. The second part presents applications and case studies in areas such as economics, finance, oceanography, climatology, environmetrics, engineering, image processing, astronomy, and biomedical science.

Covariance Tapering for Interpolation of Large Spatial Datasets

Interpolation of a spatially correlated random process is used in many scientific areas. The best unbiased linear predictor, often called a kriging predictor in geostatistical science, requires the solution of a (possibly large) linear system based on the covariance matrix of the observations. In this article, we show that tapering the correct covariance matrix with an appropriate compactly supported positive definite function reduces the computational burden significantly and still leads to an asymptotically optimal mean squared error. The effect of tapering is to create a sparse approximate linear system that can then be solved using sparse matrix algorithms. Monte Carlo simulations support the theoretical results. An application to a large climatological precipitation dataset is presented as a concrete and practical illustration.

Calibrated Probabilistic Forecasting at the Stateline Wind Energy Center: The Regime-Switching Space–Time Method

With the global proliferation of wind power, the need for accurate short-term forecasts of wind resources at wind energy sites is becoming paramount. Regime-switching space–time (RST) models merge meteorological and statistical expertise to obtain accurate and calibrated, fully probabilistic forecasts of wind speed and wind power. The model formulation is parsimonious, yet takes into account all of the salient features of wind speed: alternating atmospheric regimes, temporal and spatial correlation, diurnal and seasonal nonstationarity, conditional heteroscedasticity, and non-Gaussianity. The RST method identifies forecast regimes at a wind energy site and fits a conditional predictive model for each regime. Geographically dispersed meteorological observations in the vicinity of the wind farm are used as off-site predictors. The RST technique was applied to 2-hour-ahead forecasts of hourly average wind speed near the Stateline wind energy center in the U. S. Pacific Northwest. The RST point forecasts and distributional forecasts were accurate, calibrated, and sharp, and they compared favorably with predictions based on state-of-the-art time series techniques. This suggests that quality meteorological data from sites upwind of wind farms can be efficiently used to improve short-term forecasts of wind resources.

Highly Robust Variogram Estimation

The classical variogram estimator proposed by Matheron is not robust against outliers in the data, nor is it enough to make simple modifications such as the ones proposed by Cressie and Hawkins in order to achieve robustness. This paper proposes and studies a variogram estimator based on a highly robust estimator of scale. The robustness properties of these three estimators are analyzed and compared. Simulations with various amounts of outliers in the data are carried out. The results show that the highly robust variogram estimator improves the estimation significantly.

Powering Up With Space-Time Wind Forecasting

The technology to harvest electricity from wind energy is now advanced enough to make entire cities powered by it a reality. High-quality, short-term forecasts of wind speed are vital to making this a more reliable energy source. Gneiting et al. (2006) have introduced a model for the average wind speed two hours ahead based on both spatial and temporal information. The forecasts produced by this model are accurate, and subject to accuracy, the predictive distribution is sharp, that is, highly concentrated around its center. However, this model is split into nonunique regimes based on the wind direction at an offsite location. This paper both generalizes and improves upon this model by treating wind direction as a circular variable and including it in the model. It is robust in many experiments, such as predicting wind at other locations. We compare this with the more common approach of modeling wind speeds and directions in the Cartesian space and use a skew-t distribution for the errors. The quality of the predictions from all of these models can be more realistically assessed with a loss measure that depends upon the power curve relating wind speed to power output. This proposed loss measure yields more insight into the true value of each model’s predictions.

Generalized skew-elliptical distributions and their quadratic forms

This paper introduces generalized skew-elliptical distributions (GSE), which include the multivariate skew-normal, skew-t, skew-Cauchy, and skew-elliptical distributions as special cases. GSE are weighted elliptical distributions but the distribution of any even function in GSE random vectors does not depend on the weight function. In particular, this holds for quadratic forms in GSE random vectors. This property is beneficial for inference from non-random samples. We illustrate the latter point on a data set of Australian athletes.

Moments of skew-normal random vectors and their quadratic forms

In this paper, we derive the moments of random vectors with multivariate skew-normal distribution and their quadratic forms. Applications to time series and spatial statistics are discussed. In particular, it is shown that the moments of the sample autocovariance function and of the sample variogram estimator do not depend on the skewness vector.

Short-Term Spatio-Temporal Wind Power Forecast in Robust Look-ahead Power System Dispatch

We propose a novel statistical wind power forecast framework, which leverages the spatio-temporal correlation in wind speed and direction data among geographically dispersed wind farms. Critical assessment of the performance of spatio-temporal wind power forecast is performed using realistic wind farm data from West Texas. It is shown that spatio-temporal wind forecast models are numerically efficient approaches to improving forecast quality. By reducing uncertainties in near-term wind power forecasts, the overall cost benefits on system dispatch can be quantified. We integrate the improved forecast with an advanced robust look-ahead dispatch framework. This integrated forecast and economic dispatch framework is tested in a modified IEEE RTS 24-bus system. Numerical simulation suggests that the overall generation cost can be reduced by up to 6% using a robust look-ahead dispatch coupled with spatio-temporal wind forecast as compared with persistent wind forecast models.

Highly Robust Estimation of the Autocovariance Function

In this paper, the problem of the robustness of the sample autocovariance function is addressed. We propose a new autocovariance estimator, based on a highly robust estimator of scale. Its robustness properties are studied by means of the influence function, and a new concept of temporal breakdown point. As the theoretical variance of the estimator does not have a closed form, we perform a simulation study. Situations with various size of outliers are tested. They confirm the robustness properties of the new estimator. An S-Plus function for the highly robust autocovariance estimator is made available on the Web at http://www-math.mit.edu/~yanyuan/Genton/Time/time.html. At the end, we analyze a time series of monthly interest rates of an Austrian bank.

Spatio-temporal analysis of wildfire ignitions in the St Johns River Water Management District, Florida

We analyse the spatio-temporal structure of wildfire ignitions in the St Johns River Water Management District in north-eastern Florida. We show, using tools to analyse point patterns (e.g. the L-function), that wildfire events occur in clusters. Clustering of these events correlates with irregular distribution of fire ignitions, including lightning and human sources, and fuels on the landscape. In addition, we define a relative clustering index that summarizes the amount of clustering over various spatial scales. We carry our analysis in three steps: purely temporal, purely spatial, and spatio-temporal. Our results show that arson and lightning are the leading causes of wildfires in this region and that ignitions by railroad, lightning, and arson are spatially more clustered than ignitions by other accidental causes.