Multi-Resolution Filters for Massive Spatio-Temporal Data

Jurek, Marcin; Katzfuß, Matthias

doi:10.1080/10618600.2021.1886938

Cited by 21 publications

(26 citation statements)

References 50 publications

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“…Fourth, the marginal distributions of the x i (and hence also the variances) are exact (see Section 3.6). Fifth, V −1 has the same sparsity structure as V, which allows fast calculation of the joint posterior predictive distribution for a large number of prediction locations, and extension to Kalman-filtertype inference for massive spatio-temporal data (Jurek and Katzfuss, 2018). All of these advantages also hold for the MRA, which can be viewed as an iterative SCS approach at multiple resolutions (Katzfuss, 2017, Jurek and Katzfuss, 2018.…”

Section: Appendix C: Same Conditioning Sets (Scs)mentioning

confidence: 99%

“…Fifth, V −1 has the same sparsity structure as V, which allows fast calculation of the joint posterior predictive distribution for a large number of prediction locations, and extension to Kalman-filtertype inference for massive spatio-temporal data (Jurek and Katzfuss, 2018). All of these advantages also hold for the MRA, which can be viewed as an iterative SCS approach at multiple resolutions (Katzfuss, 2017, Jurek and Katzfuss, 2018. However, SCS and MRA may require r 1 = O( √ n z ) for accurate approximations in two-dimensional space, which results in a time complexity of O(n 3/2 z ) (Minden et al, 2017).…”

Section: Appendix C: Same Conditioning Sets (Scs)mentioning

confidence: 99%

See 1 more Smart Citation

A General Framework for Vecchia Approximations of Gaussian Processes

Katzfuß¹,

Guinness²

2021

Statist. Sci.

Self Cite

172

162

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Gaussian processes (GPs) are commonly used as models for functions, time series, and spatial fields, but they are computationally infeasible for large datasets. Focusing on the typical setting of modeling data as a GP plus an additive noise term, we propose a generalization of the Vecchia (J. Roy. Statist. Soc. Ser. B 50 (1988) 297-312) approach as a framework for GP approximations. We show that our general Vecchia approach contains many popular existing GP approximations as special cases, allowing for comparisons among the different methods within a unified framework. Representing the models by directed acyclic graphs, we determine the sparsity of the matrices necessary for inference, which leads to new insights regarding the computational properties. Based on these results, we propose a novel sparse general Vecchia approximation, which ensures computational feasibility for large spatial datasets but can lead to considerable improvements in approximation accuracy over Vecchia's original approach. We provide several theoretical results and conduct numerical comparisons. We conclude with guidelines for the use of Vecchia approximations in spatial statistics.

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Section: Appendix C: Same Conditioning Sets (Scs)mentioning

confidence: 99%

Section: Appendix C: Same Conditioning Sets (Scs)mentioning

confidence: 99%

A General Framework for Vecchia Approximations of Gaussian Processes

Katzfuß¹,

Guinness²

2021

Statist. Sci.

Self Cite

172

162

View full text Add to dashboard Cite

show abstract

“…Our methods also offer a scalable way to analyze other large spatiotemporal datasets in environmental and human health risk assessment. For example, in the air-quality research community, mobile monitoring of air pollutants is leading to high-resolution datasets with millions of observations, including campaigns in Zurich, Switzerland (Li et al (2012) Our methods could also be extended to non-Gaussian data (Zilber and Katzfuss (2021)) or online spatiotemporal filtering (Jurek and Katzfuss (2018)) using extensions or variations of the general-Vecchia framework.…”

Section: Discussionmentioning

confidence: 99%

Scalable penalized spatiotemporal land-use regression for ground-level nitrogen dioxide

Messier

Katzfuß

2021

Ann. Appl. Stat.

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Nitrogen dioxide (NO 2 ) is a primary constituent of traffic-related air pollution and has well-established harmful environmental and human-health impacts. Knowledge of the spatiotemporal distribution of NO 2 is critical for exposure and risk assessment. A common approach for assessing air pollution exposure is linear regression involving spatially referenced covariates, known as land-use regression (LUR). We develop a scalable approach for simultaneous variable selection and estimation of LUR models with spatiotemporally correlated errors, by combining a general-Vecchia Gaussianprocess approximation with a penalty on the LUR coefficients. In comparison to existing methods using simulated data, our approach resulted in higher model-selection specificity and sensitivity and in better prediction in terms of calibration and sharpness, for a wide range of relevant settings. In our spatiotemporal analysis of daily, US-wide, ground-level NO 2 data, our approach was more accurate, and produced a sparser and more interpretable model. Our daily predictions elucidate spatiotemporal patterns of NO 2 concentrations across the United States, including significant variations between cities and intra-urban variation. Thus, our predictions will be useful for epidemiological and risk-assessment studies seeking daily, national-scale predictions, and they can be used in acute-outcome health-risk assessments.

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“…Others exploit the sparsity of the precision matrix, thanks to a spatial Markovian assumption. This class includes the R packages LatticeKrig (Nychka, Bandyopadhyay, Hammerling, Lindgren, and Sain 2015;Nychka, Hammerling, Sain, and Lenssen 2019), INLA (Blangiardo, Cameletti, Baio, and Rue 2013;Lindgren and Rue 2015;Bivand, Gómez-Rubio, and Rue 2015;Rue, Martino, Blangiardo, Simpson, Riebler, and Krainski 2014) and the multi-resolution approximation approach of Katzfuss (2017), which uses the predictive pro-cess and the state space representation (Jurek and Katzfuss 2021) to model spatio-temporal data. Low-rank models are another popular approach used by spBayes.…”

Section: Statistical Softwarementioning

confidence: 99%

D-STEM v2: A Software for Modeling Functional Spatio-Temporal Data

Yaqiong¹,

Finazzi²,

Fassò³

2021

J. Stat. Soft.

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Functional spatio-temporal data naturally arise in many environmental and climate applications where data are collected in a three-dimensional space over time. The MATLAB D-STEM v1 software package was first introduced for modeling multivariate space-time data and has been recently extended to D-STEM v2 to handle functional data indexed across space and over time. This paper introduces the new modeling capabilities of D-STEM v2 as well as the complexity reduction techniques required when dealing with large data sets. Model estimation, validation and dynamic kriging are demonstrated in two case studies, one related to ground-level air quality data in Beijing, China, and the other one related to atmospheric profile data collected globally through radio sounding.

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Multi-Resolution Filters for Massive Spatio-Temporal Data

Cited by 21 publications

References 50 publications

A General Framework for Vecchia Approximations of Gaussian Processes

A General Framework for Vecchia Approximations of Gaussian Processes

Scalable penalized spatiotemporal land-use regression for ground-level nitrogen dioxide

D-STEM v2: A Software for Modeling Functional Spatio-Temporal Data

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