Estimating covariance functions of multivariate skew-Gaussian random fields on the sphere

Alegría, Alfredo; Caro, Sandra; Bevilacqua, Moreno; Porcu, Emilio; Clarke, Jorge

doi:10.1016/j.spasta.2017.07.009

Cited by 17 publications

(16 citation statements)

References 36 publications

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“…In this section, we first review the skew‐Gaussian process proposed in Zhang and El‐Shaarawi (2010). For this process, we provide an explicit expression for the finite dimensional distribution generalizing previous results in Alegría et al (2017). Then, using this skew‐Gaussian process, we propose a generalization of the t process Y ν obtaining a new process with marginal distribution of the skew‐t type (Azzalini & Capitanio, 2014).…”

Section: A Stochastic Process With Skew‐t Marginal Distributionmentioning

confidence: 82%

“…We first review the skew Gaussian process proposed in Zhang and El‐Shaarawi (2010). For this process, we provide an explicit expression of the finite dimensional distribution generalizing previous results in Alegría, Caro, Bevilacqua, Porcu, and Clarke (2017). We then propose a process with marginal distribution of the skew‐ t type (Azzalini & Capitanio, 2014) obtained through scale mixing of a skew‐Gaussian with an inverse square root process with Gamma marginals.…”

Section: Introductionmentioning

confidence: 81%

See 1 more Smart Citation

Non‐Gaussian geostatistical modeling using (skew) t processes

Bevilacqua¹,

Caamaño‐Carrillo²,

Arellano–Valle

et al. 2020

Scandinavian J Statistics

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We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with t marginals obtained through scale mixing of a Gaussian process with an inverse square root process with Gamma marginals. We then generalize this construction by considering a skew‐Gaussian process, thus obtaining a process with skew‐t marginal distributions. For the proposed (skew) t process, we study the second‐order and geometrical properties and in the t case, we provide analytic expressions for the bivariate distribution. In an extensive simulation study, we investigate the use of the weighted pairwise likelihood as a method of estimation for the t process. Moreover we compare the performance of the optimal linear predictor of the t process versus the optimal Gaussian predictor. Finally, the effectiveness of our methodology is illustrated by analyzing a georeferenced dataset on maximum temperatures in Australia.

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Section: A Stochastic Process With Skew‐t Marginal Distributionmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 81%

Non‐Gaussian geostatistical modeling using (skew) t processes

Bevilacqua¹,

Caamaño‐Carrillo²,

Arellano–Valle

et al. 2020

Scandinavian J Statistics

View full text Add to dashboard Cite

show abstract

“…The Gaussian assumption makes a spatial model simple in structure and facilitates statistical predictions, but this assumption is often not supported by the data. To deal with this issue, we may consider non-Gaussian processes (Du et al, 2012, Ma, 2013a, 2013b, 2015, Du, Ma and Li, 2013), such as the skew-Gaussian (Alegría et al, 2017a) and the Tukey gand-h random fields (Xu and Genton, 2017). These are promising for various applications, but their implementation remains unexplored.…”

Section: Discussionmentioning

confidence: 99%

Spherical Process Models for Global Spatial Statistics

2017

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Abstract. Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture the spatial and temporal behavior of these global data sets. Though the geodesic distance is the most natural metric for measuring distance on the surface of a sphere, mathematical limitations have compelled statisticians to use the chordal distance to compute the covariance matrix in many applications instead, which may cause physically unrealistic distortions. Therefore, covariance functions directly defined on a sphere using the geodesic distance are needed. We discuss the issues that arise when dealing with spherical data sets on a global scale and provide references to recent literature. We review the current approaches to building process models on spheres, including the differential operator, the stochastic partial differential equation, the kernel convolution, and the deformation approaches. We illustrate realizations obtained from Gaussian processes with different covariance structures and the use of isotropic and nonstationary covariance models through deformations and geographical indicators for global surface temperature data. To assess the suitability of each method, we compare their log-likelihood values and prediction scores, and we end with a discussion of related research problems.

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“…With some variations, the related optimal interpolation algorithm is based on the autocovariance function or, equivalently, on the structure function (Sofieva et al, 2008). This approach is often used to interpolate in spaces of increasing complexity, such as the Euclidean plane, the sphere (Alegria et al, 2017), the three-dimensional Euclidean space, or the circular shell representing the atmosphere (Porcu et al, 2016). Interestingly, it can be shown that the spline interpolation is a special case of the GP interpolation (Kimeldorf and Wahba, 1970).…”

Section: Introductionmentioning

confidence: 99%

Interpolation uncertainty of atmospheric temperature profiles

2020

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Abstract. This paper is motivated by the fact that, although temperature readings made by Vaisala RS41 radiosondes at GRUAN sites (https://www.gruan.org/, last access: 30 November 2020) are given at 1 s resolution, for various reasons, missing data are spread along the atmospheric profile. Such a problem is quite common with radiosonde data and other profile data. Hence, (linear) interpolation is often used to fill the gaps in published data products. From this perspective, the present paper considers interpolation uncertainty, using a statistical approach to understand the consequences of substituting missing data with interpolated data. In particular, a general framework for the computation of interpolation uncertainty based on a Gaussian process (GP) set-up is developed. Using the GP characteristics, a simple formula for computing the linear interpolation standard error is given. Moreover, the GP interpolation is proposed as it provides an alternative interpolation method with its standard error. For the Vaisala RS41, the two approaches are shown to provide similar interpolation performances using an extensive cross-validation approach based on the block-bootstrap technique. Statistical results about interpolation uncertainty at various GRUAN sites and for various missing gap lengths are provided. Since both approaches result in an underestimation of the interpolation uncertainty, a bootstrap-based correction formula is proposed. Using the root mean square error, it is found that, for short gaps, with an average length of 5 s, the average uncertainty is less than 0.10 K. For larger gaps, it increases up to 0.35 K for an average gap length of 30 s and up to 0.58 K for a gap of 60 s. It is concluded that this approach could be implemented in a future version of the GRUAN data processing.

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Estimating covariance functions of multivariate skew-Gaussian random fields on the sphere

Cited by 17 publications

References 36 publications

Non‐Gaussian geostatistical modeling using (skew) t processes

Non‐Gaussian geostatistical modeling using (skew) t processes

Spherical Process Models for Global Spatial Statistics

Interpolation uncertainty of atmospheric temperature profiles

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