Efficient Estimation of Non-stationary Spatial Covariance Functions with Application to High-resolution Climate Model Emulation

Li, Yuxiao; Sun, Ying

doi:10.5705/ss.202017.0536

Cited by 8 publications

(6 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Datasets 1a-2 (100K) and 1b-2 (1M) were generated at irregular locations from a zero-mean Gaussian process Z(s) with a nonstationary Matérn covariance function (Li and Sun, 2019, and references therein):…”

Section: Univariate Nonstationary Spatial Model (Sub-competitions 1a ...mentioning

confidence: 99%

The Second Competition on Spatial Statistics for Large Datasets

Abdulah¹,

Alamri²,

Nag³

et al. 2022

Journal of Data Science

View full text Add to dashboard Cite

In the last few decades, the size of spatial and spatio-temporal datasets in many research areas has rapidly increased with the development of data collection technologies. As a result, classical statistical methods in spatial statistics are facing computational challenges. For example, the kriging predictor in geostatistics becomes prohibitive on traditional hardware architectures for large datasets as it requires high computing power and memory footprint when dealing with large dense matrix operations. Over the years, various approximation methods have been proposed to address such computational issues, however, the community lacks a holistic process to assess their approximation efficiency. To provide a fair assessment, in 2021, we organized the first competition on spatial statistics for large datasets, generated by our ExaGeoStat software, and asked participants to report the results of estimation and prediction. Thanks to its widely acknowledged success and at the request of many participants, we organized the second competition in 2022 focusing on predictions for more complex spatial and spatio-temporal processes, including univariate nonstationary spatial processes, univariate stationary space-time processes, and bivariate stationary spatial processes. In this paper, we describe in detail the data generation procedure and make the valuable datasets publicly available for a wider adoption. Then, we review the submitted methods from fourteen teams worldwide, analyze the competition outcomes, and assess the performance of each team.

show abstract

Section: Univariate Nonstationary Spatial Model (Sub-competitions 1a ...mentioning

confidence: 99%

The Second Competition on Spatial Statistics for Large Datasets

Abdulah¹,

Alamri²,

Nag³

et al. 2022

Journal of Data Science

View full text Add to dashboard Cite

show abstract

“…Hauser et al (2012) discussed how ANNs can be used in Bayesian calibration of climate models. Li and Sun (2019) developed a new efficient way of estimating nonstationary mean and/or covariance functions (e.g., in connection with transition between the land and the ocean or between mountains and plains) with application to high-resolution climate model emulation. Using local polynomial approximation of spatially varying parameters in the Matérn covariance function, they proposed a maximum-likelihood estimation procedure and applied it to analyzing precipitation data.…”

Section: Statistical Inference and Machine Learning For Emulating Cli...mentioning

confidence: 99%

Statistical mechanics in climate emulation: Challenges and perspectives

Sudakow

Pokojovy

Lyakhov

2022

Environ. Data Science

View full text Add to dashboard Cite

Climate emulators are a powerful instrument for climate modeling, especially in terms of reducing the computational load for simulating spatiotemporal processes associated with climate systems. The most important type of emulators are statistical emulators trained on the output of an ensemble of simulations from various climate models. However, such emulators oftentimes fail to capture the “physics” of a system that can be detrimental for unveiling critical processes that lead to climate tipping points. Historically, statistical mechanics emerged as a tool to resolve the constraints on physics using statistics. We discuss how climate emulators rooted in statistical mechanics and machine learning can give rise to new climate models that are more reliable and require less observational and computational resources. Our goal is to stimulate discussion on how statistical climate emulators can further be improved with the help of statistical mechanics which, in turn, may reignite the interest of statistical community in statistical mechanics of complex systems.

show abstract

“…This last feature is potentially the most problematic, since joint predictions are required for uncertainty quantification of spatial averages as well as generating statistical ensembles of the underlying process of interest (see, e.g. [41]). This important trade-off between computational speed and approximation accuracy/joint prediction is the primary reason why we have chosen to include both of these methods in this paper (and the corresponding software package), as the specific application may motivate a preference for speed vs. accuracy, and furthermore if joint predictions are required or not.…”

Section: Comparing Sgv and Nngp-rmentioning

confidence: 99%

Bayesian inference for high-dimensional nonstationary Gaussian processes

Risser

Turek

2020

Journal of Statistical Computation and Simulation

View full text Add to dashboard Cite

In spite of the diverse literature on nonstationary spatial modelling and approximate Gaussian process (GP) methods, there are no general approaches for conducting fully Bayesian inference for moderately sized nonstationary spatial data sets on a personal laptop. For statisticians and data scientists who wish to conduct posterior inference and prediction with appropriate uncertainty quantification, the lack of such approaches and software is a limitation. Here, we develop methodology for implementing formal Bayesian inference for a general class of nonstationary GPs. Our novel approach uses preexisting frameworks for characterizing nonstationarity in a new way while utilizing via modern GP likelihood approximations. Posterior sampling is implemented using flexible MCMC methods, with nonstationary posterior prediction conducted as a post-processing step. We demonstrate our novel methods on two data sets, ranging from several hundred to several thousand locations. All of our methods are implemented in the freely available BayesNSGP software package for R.

show abstract

Efficient Estimation of Non-stationary Spatial Covariance Functions with Application to High-resolution Climate Model Emulation

Cited by 8 publications

References 27 publications

The Second Competition on Spatial Statistics for Large Datasets

The Second Competition on Spatial Statistics for Large Datasets

Statistical mechanics in climate emulation: Challenges and perspectives

Bayesian inference for high-dimensional nonstationary Gaussian processes

Contact Info

Product

Resources

About