|   | 
Details
   web
Records
Author Bachoc, F.; Porcu, E.; Bevilacqua, M.; Furrer, R.; Faouzi, T.
Title Asymptotically equivalent prediction in multivariate geostatistics Type
Year 2022 Publication (up) Bernoulli Abbreviated Journal Bernoulli
Volume 28 Issue 4 Pages 2518-2545
Keywords Cokriging; equivalence of Gaussian measures; fixed domain asymptotics; functional analysis; Generalized Wendland; Matern; spectral analysis
Abstract Cokriging is the common method of spatial interpolation (best linear unbiased prediction) in multivariate geo-statistics. While best linear prediction has been well understood in univariate spatial statistics, the literature for the multivariate case has been elusive so far. The new challenges provided by modern spatial datasets, being typ-ically multivariate, call for a deeper study of cokriging. In particular, we deal with the problem of misspecified cokriging prediction within the framework of fixed domain asymptotics. Specifically, we provide conditions for equivalence of measures associated with multivariate Gaussian random fields, with index set in a compact set of a d-dimensional Euclidean space. Such conditions have been elusive for over about 50 years of spatial statistics. We then focus on the multivariate Matern and Generalized Wendland classes of matrix valued covariance functions, that have been very popular for having parameters that are crucial to spatial interpolation, and that control the mean square differentiability of the associated Gaussian process. We provide sufficient conditions, for equivalence of Gaussian measures, relying on the covariance parameters of these two classes. This enables to identify the parameters that are crucial to asymptotically equivalent interpolation in multivariate geostatistics. Our findings are then illustrated through simulation studies.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1350-7265 ISBN Medium
Area Expedition Conference
Notes WOS:000843190100015 Approved
Call Number UAI @ alexi.delcanto @ Serial 1639
Permanent link to this record
 

 
Author Caamaño-Carrillo, C.; Bevilacqua, M.; López, C.; Morales-Oñate, V.
Title Nearest neighbors weighted composite likelihood based on pairs for (non-)Gaussian massive spatial data with an application to Tukey-hh random fields estimation Type
Year 2024 Publication (up) Computational Statistics & Data Analysis Abbreviated Journal Comput. Stat. Data Anal.
Volume 191 Issue Pages 107887
Keywords Covariance estimation; Geostatistics; Large datasets; Vecchia approximation
Abstract A highly scalable method for (non-)Gaussian random fields estimation is proposed. In particular, a novel (a) symmetric weight function based on nearest neighbors for the method of maximum weighted composite likelihood based on pairs (WCLP) is studied. The new weight function allows estimating massive (up to millions) spatial datasets and improves the statistical efficiency of the WCLP method using symmetric weights based on distances, as shown in the numerical examples. As an application of the proposed method, the estimation of a novel non-Gaussian random field named Tukey-hh random field that has flexible marginal distributions (possibly skewed and/or heavy-tailed) is considered. In an extensive simulation study the statistical efficiency of the proposed nearest neighbors WCLP method with respect to the WCLP method using weights based on distances is explored when estimating the parameters of the Tukey-hh random field. In the Gaussian case the proposed method is compared with the Vecchia approximation from computational and statistical viewpoints. Finally, the effectiveness of the proposed methodology is illustrated by estimating a large dataset of mean temperatures in South -America. The proposed methodology has been implemented in an open-source package for the R statistical environment.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0167-9473 ISBN Medium
Area Expedition Conference
Notes WOS:001166253600001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1956
Permanent link to this record
 

 
Author Morales-Onate, V.; Crudu, F.; Bevilacqua, M.
Title Blockwise Euclidean likelihood for spatio-temporal covariance models Type
Year 2021 Publication (up) Econometrics and Statistics Abbreviated Journal Econ. Stat.
Volume 20 Issue Pages 176-201
Keywords Composite likelihood; Euclidean likelihood; Gaussian random fields; Parallel computing; OpenCL
Abstract A spatio-temporal blockwise Euclidean likelihood method for the estimation of covariance models when dealing with large spatio-temporal Gaussian data is proposed. The method uses moment conditions coming from the score of the pairwise composite likelihood. The blockwise approach guarantees considerable computational improvements over the standard pairwise composite likelihood method. In order to further speed up computation, a general purpose graphics processing unit implementation using OpenCL is implemented. The asymptotic properties of the proposed estimator are derived and the finite sample properties of this methodology by means of a simulation study highlighting the computational gains of the OpenCL graphics processing unit implementation. Finally, there is an application of the estimation method to a wind component data set. (C) 2021 EcoSta Econometrics and Statistics. Published by Elsevier B.V. All rights reserved.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 2468-0389 ISBN Medium
Area Expedition Conference
Notes WOS:000689351000012 Approved
Call Number UAI @ alexi.delcanto @ Serial 1460
Permanent link to this record
 

 
Author Bevilacqua, M.; Camano-Carrillo, C.; Porcu, E.
Title Unifying compactly supported and Matern covariance functions in spatial statistics Type
Year 2022 Publication (up) Journal of Multivariate Analysis Abbreviated Journal J. Multivar. Anal.
Volume 189 Issue Pages 104949
Keywords Gaussian random fields; Generalized wendland model; Fixed domain asymptotics; Sparse matrices
Abstract The Matern family of covariance functions has played a central role in spatial statistics for decades, being a flexible parametric class with one parameter determining the smoothness of the paths of the underlying spatial field. This paper proposes a family of spatial covariance functions, which stems from a reparameterization of the generalized Wendland family. As for the Matern case, the proposed family allows for a continuous parameterization of the smoothness of the underlying Gaussian random field, being additionally compactly supported.

More importantly, we show that the proposed covariance family generalizes the Matern model which is attained as a special limit case. This implies that the (reparametrized) Generalized Wendland model is more flexible than the Matern model with an extra-parameter that allows for switching from compactly to globally supported covariance functions.

Our numerical experiments elucidate the speed of convergence of the proposed model to the Matern model. We also inspect the asymptotic distribution of the maximum likelihood method when estimating the parameters of the proposed covariance models under both increasing and fixed domain asymptotics. The effectiveness of our proposal is illustrated by analyzing a georeferenced dataset of mean temperatures over a region of French, and performing a re-analysis of a large spatial point referenced dataset of yearly total precipitation anomalies.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0047-259X ISBN Medium
Area Expedition Conference
Notes WOS:000759649300026 Approved
Call Number UAI @ alexi.delcanto @ Serial 1542
Permanent link to this record
 

 
Author Morales-Navarrete, D.; Bevilacqua, M.; Caamano-Carrillo, C.; Castro, L.M.
Title Modeling Point Referenced Spatial Count Data: A Poisson Process Approach Type
Year 2023 Publication (up) Journal of the American Statistical Association Abbreviated Journal J. Am. Stat. Assoc.
Volume Early Access Issue Pages
Keywords Gaussian copula; Gaussian random field; Pairwise likelihood function; Poisson distribution; Renewal process
Abstract Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and mathematical tractability. However, this assumption seems to be restrictive when dealing with counting data. To deal with this situation, we propose a random field with a Poisson marginal distribution considering a sequence of independent copies of a random field with an exponential marginal distribution as “inter-arrival times ” in the counting renewal processes framework. Our proposal can be viewed as a spatial generalization of the Poisson counting process. Unlike the classical hierarchical Poisson Log-Gaussian model, our proposal generates a (non)-stationary random field that is mean square continuous and with Poisson marginal distributions. For the proposed Poisson spatial random field, analytic expressions for the covariance function and the bivariate distribution are provided. In an extensive simulation study, we investigate the weighted pairwise likelihood as a method for estimating the Poisson random field parameters. Finally, the effectiveness of our methodology is illustrated by an analysis of reindeer pellet-group survey data, where a zero-inflated version of the proposed model is compared with zero-inflated Poisson Log-Gaussian and Poisson Gaussian copula models. for this article, including technical proofs and R code for reproducing the work, are available as an online supplement.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0162-1459 ISBN Medium
Area Expedition Conference
Notes WOS:000892551000001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1698
Permanent link to this record
 

 
Author Blasi, F.; Caamano-Carrillo, C.; Bevilacqua, M.; Furrer, R.
Title A selective view of climatological data and likelihood estimation Type
Year 2022 Publication (up) Spatial Statistics Abbreviated Journal Spat. Stat.
Volume 50 Issue SI Pages 100596
Keywords Tapering; Composite likelihood; Sinh-arcsinh distribution; CMIP6 data; Random field; Spatial process
Abstract This article gives a narrative overview of what constitutes climatological data and their typical features, with a focus on aspects relevant to statistical modeling. We restrict the discussion to univariate spatial fields and focus on maximum likelihood estimation. To address the problem of enormous datasets, we study three common approximation schemes: tapering, direct misspecification, and composite likelihood for Gaussian and nonGaussian distributions. We focus particularly on the so-called 'sinh-arcsinh distribution', obtained through a specific transformation of the Gaussian distribution. Because it has flexible marginal distributions – possibly skewed and/or heavy-tailed – it has a wide range of applications. One appealing property of the transformation involved is the existence of an explicit inverse transformation that makes likelihood-based methods straightforward. We describe a simulation study illustrating the effects of the different approximation schemes. To the best of our knowledge, a direct comparison of tapering, direct misspecification, and composite likelihood has never been made previously, and we show that direct misspecification is inferior. In some metrics, composite likelihood has a minor advantage over tapering. We use the estimation approaches to model a high-resolution global climate change field. All simulation code is available as a Docker container and is thus fully reproducible. Additionally, the present article describes where and how to get various climate datasets. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 2211-6753 ISBN Medium
Area Expedition Conference
Notes WOS:000822683400023 Approved
Call Number UAI @ alexi.delcanto @ Serial 1619
Permanent link to this record
 

 
Author Faouzi, T.; Porcu, E.; Bevilacqua, M.
Title SPACE-TIME ESTIMATION AND PREDICTION UNDER FIXED-DOMAIN ASYMPTOTICS WITH COMPACTLY SUPPORTED COVARIANCE FUNCTIONS Type
Year 2022 Publication (up) Statistica Sinica Abbreviated Journal Stat. Sin.
Volume 32 Issue 3 Pages 1187-1203
Keywords Fixed-domain asymptotics; microergodic parameter; maximum likelihood; space-time generalized wendland family
Abstract We study the estimation and prediction of Gaussian processes with spacetime covariance models belonging to the dynamical generalized Wendland (DGW) family, under fixed-domain asymptotics. Such a class is nonseparable, has dynamical compact supports, and parameterizes differentiability at the origin similarly to the space-time Matern class.

Our results are presented in two parts. First, we establish the strong consistency and asymptotic normality for the maximum likelihood estimator of the microergodic parameter associated with the DGW covariance model, under fixed-domain asymptotics. The second part focuses on optimal kriging prediction under the DGW model and an asymptotically correct estimation of the mean squared error using a misspecified model. Our theoretical results are, in turn, based on the equivalence of Gaussian measures under some given families of space-time covariance functions, where both space or time are compact. The technical results are provided in the online Supplementary material.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1017-0405 ISBN Medium
Area Expedition Conference
Notes WOS:000818975200001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1599
Permanent link to this record
 

 
Author Faouzi, T.; Porcu, E.; Kondrashuk, I.; Bevilacqua, M.
Title Convergence arguments to bridge cauchy and matern covariance functions Type
Year 2023 Publication (up) Statistical Papers Abbreviated Journal Stat. Pap.
Volume Early Access Issue Pages
Keywords Mellin-Barnes transforms; Positive definite; Spectral densities; Random field
Abstract The Matern and the Generalized Cauchy families of covariance functions have a prominent role in spatial statistics as well as in a wealth of statistical applications. The Matern family is crucial to index mean-square differentiability of the associated Gaussian random field; the Cauchy family is a decoupler of the fractal dimension and Hurst effect for Gaussian random fields that are not self-similar. Our effort is devoted to prove that a scale-dependent family of covariance functions, obtained as a reparameterization of the Generalized Cauchy family, converges to a particular case of the Matern family, providing a somewhat surprising bridge between covariance models with light tails and covariance models that allow for long memory effect.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0932-5026 ISBN Medium
Area Expedition Conference
Notes WOS:000936708800003 Approved
Call Number UAI @ alexi.delcanto @ Serial 1753
Permanent link to this record
 

 
Author Bevilacqua, M.; Caamano-Carrillo, C.; Arellano-Valle, R.B.; Gomez, C.
Title A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers Type
Year 2022 Publication (up) Test Abbreviated Journal Test
Volume 31 Issue 3 Pages 644-674
Keywords Asymmetric random fields; Composite likelihood; Spatial outliers; Tukey-h distribution
Abstract In this paper, we propose a new class of non-Gaussian random fields named two-piece random fields. The proposed class allows to generate random fields that have flexible marginal distributions, possibly skewed and/or heavy-tailed and, as a consequence, has a wide range of applications. We study the second-order properties of this class and provide analytical expressions for the bivariate distribution and the associated correlation functions. We exemplify our general construction by studying two examples: two-piece Gaussian and two-piece Tukey-h random fields. An interesting feature of the proposed class is that it offers a specific type of dependence that can be useful when modeling data displaying spatial outliers, a property that has been somewhat ignored from modeling viewpoint in the literature for spatial point referenced data. Since the likelihood function involves analytically intractable integrals, we adopt the weighted pairwise likelihood as a method of estimation. The effectiveness of our methodology is illustrated with simulation experiments as well as with the analysis of a georeferenced dataset of mean temperatures in Middle East.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1133-0686 ISBN Medium
Area Expedition Conference
Notes WOS:000739261700001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1518
Permanent link to this record