Marc G. Genton

Marc G. Genton
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Marc G. Genton

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Statistics - Methodology (10)
Statistics - Applications (7)
Statistics - Computation (4)
Statistics - Theory (3)
Mathematics - Statistics (3)
Physics - Atmospheric and Oceanic Physics (1)
Statistics - Machine Learning (1)

Publications Authored By Marc G. Genton

The classification of multivariate functional data is an important task in scientific research. Unlike point-wise data, functional data are usually classified by their shapes rather than by their scales. We define an outlyingness matrix by extending directional outlyingness, an effective measure of the shape variation of curves that combines the direction of outlyingness with conventional depth. Read More

We show how to perform full likelihood inference for max-stable multivariate distributions or processes based on a stochastic Expectation-Maximisation algorithm. In contrast to current approaches, such as pairwise likelihoods or the Stephenson--Tawn likelihood, our method combines statistical and computational efficiency in high-dimensions, and it is not subject to bias entailed by lack of convergence of the underlying partition. The good performance of this methodology is demonstrated by simulation based on the logistic model, and it is shown to provide dramatic computational time improvements with respect to a direct computation of the likelihood. Read More

This article proposes a new graphical tool, the magnitude-shape (MS) plot, for visualizing both the magnitude and shape outlyingness of multivariate functional data. The proposed tool builds on the recent notion of functional directional outlyingness, which measures the centrality of functional data by simultaneously considering the level and the direction of their deviation from the central region. The MS-plot intuitively presents not only levels but also directions of magnitude outlyingness on the horizontal axis or plane, and demonstrates shape outlyingness on the vertical axis. Read More

Facing increasing domestic energy consumption from population growth and industrialization, Saudi Arabia is aiming to reduce its reliance on fossil fuels and to broaden its energy mix by expanding investment in renewable energy sources, including wind energy. A preliminary task in the development of wind energy infrastructure is the assessment of wind energy potential, a key aspect of which is the characterization of its spatio-temporal behavior. In this study we examine the impact of internal climate variability on seasonal wind power density fluctuations using 30 simulations from the Large Ensemble Project (LENS) developed at the National Center for Atmospheric Research. Read More

Wind has the potential to make a significant contribution to future energy resources; however, the task of locating the sources of this renewable energy on a global scale with climate models, along with the associated uncertainty, is hampered by the storage challenges associated with the extremely large amounts of computer output. Various data compression techniques can be used to mitigate this problem, but traditional algorithms deliver relatively small compression rates by focusing on individual simulations. We propose a statistical model that aims at reproducing the data-generating mechanism of an ensemble of runs by providing a stochastic approximation of global annual wind data and compressing all the scientific information in the estimated statistical parameters. Read More

The direction of outlyingness is crucial to describing the centrality of multivariate functional data. Motivated by this idea, we propose a new framework that combines classical depth with the direction of outlyingness. We generalize classical depth to directional outlyingness for both point-wise and functional data. Read More

We propose a new copula model for replicated multivariate spatial data. Unlike classical models that assume multivariate normality of the data, the proposed copula is based on the assumption that some factors exist that affect the joint spatial dependence of all measurements of each variable as well as the joint dependence among these variables. The model is parameterized in terms of a cross-covariance function that may be chosen from the many models proposed in the literature. Read More

Functional Magnetic Resonance Imaging (fMRI) is a primary modality for studying brain activity. Modeling spatial dependence of imaging data at different scales is one of the main challenges of contemporary neuroimaging, and it could allow for accurate testing for significance in neural activity. The high dimensionality of this type of data (on the order of hundreds of thousands of voxels) poses serious modeling challenges and considerable computational constraints. Read More

We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy tails and asymmetry. We propose a general non-informative prior structure for these regression models and show that the corresponding posterior distribution is proper under mild conditions. Read More

We propose a new copula model that can be used with replicated spatial data. Unlike the multivariate normal copula, the proposed copula is based on the assumption that a common factor exists and affects the joint dependence of all measurements of the process. Moreover, the proposed copula can model tail dependence and tail asymmetry. Read More

Rejoinder of ``Cross-Covariance Functions for Multivariate Geostatistics'' by Genton and Kleiber [arXiv:1507.08017]. Read More

Continuously indexed datasets with multiple variables have become ubiquitous in the geophysical, ecological, environmental and climate sciences, and pose substantial analysis challenges to scientists and statisticians. For many years, scientists developed models that aimed at capturing the spatial behavior for an individual process; only within the last few decades has it become commonplace to model multiple processes jointly. The key difficulty is in specifying the cross-covariance function, that is, the function responsible for the relationship between distinct variables. Read More

Tukey's $g$-and-$h$ distribution has been a powerful tool for data exploration and modeling since its introduction. However, two long standing challenges associated with this distribution family have remained unsolved until this day: how to find an optimal estimation procedure and how to make valid statistical inference on unknown parameters. To overcome these two challenges, a computationally efficient estimation procedure based on maximizing an approximated likelihood function of the Tukey's $g$-and-$h$ distribution is proposed and is shown to have the same estimation efficiency as the maximum likelihood estimator under mild conditions. Read More

We develop a multi-level restricted Gaussian maximum likelihood method for estimating the covariance function parameters and computing the best unbiased predictor. Our approach produces a new set of multi-level contrasts where the deterministic parameters of the model are filtered out thus enabling the estimation of the covariance parameters to be decoupled from the deterministic component. Moreover, the multi-level covariance matrix of the contrasts exhibit fast decay that is dependent on the smoothness of the covariance function. Read More

Accurate short-term wind speed forecasting is needed for the rapid development and efficient operation of wind energy resources. This is, however, a very challenging problem. Although on the large scale, the wind speed is related to atmospheric pressure, temperature, and other meteorological variables, no improvement in forecasting accuracy was found by incorporating air pressure and temperature directly into an advanced space-time statistical forecasting model, the trigonometric direction diurnal (TDD) model. Read More

The main approach to inference for multivariate extremes consists in approximating the joint upper tail of the observations by a parametric family arising in the limit for extreme events. The latter may be expressed in terms of componentwise maxima, high threshold exceedances or point processes, yielding different but related asymptotic characterizations and estimators. The present paper clarifies the connections between the main likelihood estimators, and assesses their practical performance. Read More

Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable models have been developed, and fitted to various types of data. However, a recurrent problem is the modeling of non-stationarity. Read More

In multivariate or spatial extremes, inference for max-stable processes observed at a large collection of locations is among the most challenging problems in computational statistics, and current approaches typically rely on less expensive composite likelihoods constructed from small subsets of data. In this work, we explore the limits of modern state-of-the-art computational facilities to perform full likelihood inference and to efficiently evaluate high-order composite likelihoods. With extensive simulations, we assess the loss of information of composite likelihood estimators with respect to a full likelihood approach for some widely-used multivariate or spatial extreme models, we discuss how to choose composite likelihood truncation to improve the efficiency, and we also provide recommendations for practitioners. Read More

We examine some distributions used extensively within the model-based clustering literature in recent years, paying special attention to} claims that have been made about their relative efficacy. Theoretical arguments are provided as well as real data examples. Read More

We study the asymptotic joint distribution of sample space--time covariance estimators of strictly stationary random fields. We do this without any marginal or joint distributional assumptions other than mild moment and mixing conditions. We consider several situations depending on whether the observations are regularly or irregularly spaced and whether one part or the whole domain of interest is fixed or increasing. Read More