Towards a complete picture of stationary covariance functions on spheres cross time

White, Philip A.; Porcu, Emilio

doi:10.1214/19-ejs1593

Cited by 24 publications

(20 citation statements)

References 67 publications

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“…Then, we consider two examples based on the class of space-circular time nonseparable covariance models presented by Shirota and Gelfand (2017) (Models 4 and 5), where Model 4 ignores temporal decay and Model 5 is an example of construction (B). Then, we give two examples of nonseparable circular cross linear time covariance models, one from White and Porcu (2018) and the other from Theorem 1, where both models are multiplied by an exponential spatial covariance function Note. MAPE = mean absolute prediction error; RMSPE = root-mean-squared prediction error; CVG = prediction interval coverage.…”

Section: Resultsmentioning

confidence: 99%

“…For construction (B), space-circular time nonseparability, Shirota and Gelfand (2017) propose using C 3 (h, ) =  2 (h 2 , ) to account for the interaction between circular time lags and spatial differences. Other appropriate models for C 3 (h, ) are given by theorem 2 in the work of White and Porcu (2018), which shows that C 3 (h, ) =  2 ( , h 2 ) is positive definite, and theorem 1 in the work of Porcu et al (2016), which proves that C 3 (h, ) = (h 2 , ) is a valid covariance function. The classes proposed in Porcu et al (2016) and White and Porcu (2018) can also be used for circular-linear time nonseparability (i.e., for construction (C), replace h with u to obtain C 5 ( , u)).…”

mentioning

confidence: 99%

“…Other appropriate models for C 3 (h, ) are given by theorem 2 in the work of White and Porcu (2018), which shows that C 3 (h, ) =  2 ( , h 2 ) is positive definite, and theorem 1 in the work of Porcu et al (2016), which proves that C 3 (h, ) = (h 2 , ) is a valid covariance function. The classes proposed in Porcu et al (2016) and White and Porcu (2018) can also be used for circular-linear time nonseparability (i.e., for construction (C), replace h with u to obtain C 5 ( , u)). Additional choices for C 5 ( , u) of construction (C) are the core of our theoretical contributions in Section 3.2.…”

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confidence: 99%

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Nonseparable covariance models on circles cross time: A study of Mexico City ozone

White

Porcu

2019

Environmetrics

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We propose a continuous spatiotemporal model for Mexico City ozone levels that account for distinct daily seasonality, as well as variation across the city and over the peak ozone season (April and May) of 2017. To account for these patterns, we use covariance models over space, circles, and time. We review relevant existing covariance models and develop new classes of nonseparable covariance models appropriate for seasonal data collected at many locations. We compare the predictive performance of a variety of models that utilize various nonseparable covariance functions. We use the best model to predict hourly ozone levels at unmonitored locations in April and May to infer compliance with Mexican air quality standards and to estimate the respiratory health risk associated with ozone exposure. We find that predicted compliance with air quality standards and estimated respiratory health risk vary greatly over space and time. In some regions, we predict exceedance of national standards for more than a third of the hours in April and May, and on many days, we predict that nearly all of Mexico City exceeds nationally legislated ozone thresholds at least once. In southern Mexico City, we estimate the respiratory risk for ozone to be 55% higher, on average, than the annual average risk and as much at 170% higher on some days.

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Section: Resultsmentioning

confidence: 99%

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confidence: 99%

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Nonseparable covariance models on circles cross time: A study of Mexico City ozone

White

Porcu

2019

Environmetrics

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“…Because most real-world processes exhibit nonseparable relationships between spatial quantities or between space and time (see, e.g., Cressie & Huang, 1999;Gneiting, 2002;Gneiting, Genton, & Guttorp, 2006;Kolovos, Christakos, Hristopulos, & Serre, 2004, for similar arguments), we consider nonseparable covariance functions that could account for spatial relationships. Specifically, we adapt classes of covariance functions designed for nonseparable space-time relationships from Porcu, Bevilacqua, and Genton (2016) and White and Porcu (2018) to nonseparable space-elevation change relationships.…”

Section: A2 Model Selection Resultsmentioning

confidence: 99%

A model for Antarctic surface mass balance and ice core site selection

et al. 2019

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In this study, we develop a model for Antarctic surface mass balance (SMB), which allows us to assess regional and global uncertainty in SMB estimation and carry out a model‐based design to propose new measurement sites. For this analysis, we use a quality‐controlled aggregate data set of SMB field measurements with significantly more observations than previous analyses; however, many of the measurements in this data set lack quality ratings. In addition, these data demonstrate spatial autocorrelation, heteroscedasticity, and non‐Gaussianity. To account for these data attributes, we pose a Bayesian Gaussian process generalized linear model for SMB. To address missing reliability ratings, we use a mixture model with different variances to add robustness to our model. In addition, we present a novel approach for modeling the variance as a function of the mean to account for the heteroscedasticity in the data. Using this model, we predict Antarctic SMB and compare our estimates with previous estimates. In addition, we create prediction maps with uncertainty to visualize spatial patterns in SMB and to identify regions of high SMB uncertainty. Our model estimates the total SMB to be 2,156 Gton/yr over the range of our data, with 95% credible interval (2,081, 2,234) Gton/yr. Overall, our results suggest lower Antarctic SMB than previously reported. This lower SMB estimate may be indicative of a more dire diagnosis of the long‐term health of the Antarctic ice sheets. Lastly, we use our model to propose 25 new measurement sites for the field study utilizing a sequential design, minimizing the integrated mean squared error.

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“…for all d and m were shown recently in [27]. In [21], Schlather has considered diagonalized versionsG α (t) :…”

Section: Introductionmentioning

confidence: 99%

Gneiting Class, Semi-Metric Spaces and Isometric Embeddings

Menegatto

Oliveira

Porcu

2020

Constructive Mathematical Analysis

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This paper revisits the Gneiting class of positive definite kernels originally proposed as a class of covariance functions for space-time processes. Under the framework of quasi-metric spaces and isometric embeddings, the paper proposes a general and unifying framework that encompasses results provided by earlier literature. Our results allow to study the positive definiteness of the Gneiting class over products of either Euclidean spaces or high dimensional spheres and quasi-metric spaces. In turn, Gneiting's theorem is proved here by a direct construction, eluding Fourier inversion (the so-called Gneiting's lemma) and convergence arguments that are required by Gneiting to preserve an integrability assumption.

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Towards a complete picture of stationary covariance functions on spheres cross time

Cited by 24 publications

References 67 publications

Nonseparable covariance models on circles cross time: A study of Mexico City ozone

Nonseparable covariance models on circles cross time: A study of Mexico City ozone

A model for Antarctic surface mass balance and ice core site selection

Gneiting Class, Semi-Metric Spaces and Isometric Embeddings

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