Gridding and Parameter Expansion for Scalable Latent Gaussian Models of Spatial Multivariate Data

Area of Science:

• Computational Statistics
• Spatial Statistics
• Machine Learning

Background:

• Scalable spatial Gaussian processes (GPs) are crucial for analyzing massive datasets.
• Sparse Directed Acyclic Graphs (DAGs) offer a framework for spatial dependence but can lead to issues in covariance parameter estimation.
• Existing Markov chain Monte Carlo (MCMC) algorithms may exhibit pathological behavior, limiting their practical performance.

Purpose of the Study:

• To introduce novel methods, gridding and parameter expansion, to improve MCMC algorithm performance for spatial GPs.
• To enhance the effective sample size per unit time (ESS/s) in MCMC sampling for large-scale spatial data.
• To address computational challenges in analyzing high-resolution spatial data and massive datasets.

Main Methods:

• Development and application of a gridding strategy, a model-based approach to reduce computational costs for irregularly spaced data.
• Implementation of parameter expansion to reduce posterior sample dependence in spatial regression models for high-resolution data.
• Utilizing sparse DAGs for spatial dependence characterization and fast posterior sampling algorithms.

Main Results:

• Gridding and parameter expansion significantly improve the practical performance of MCMC algorithms, increasing ESS/s.
• These strategies yield substantial computational gains, particularly in big data settings.
• The proposed methods demonstrate effectiveness in analyzing synthetic datasets with Matérn covariance functions and coregionalization models.

Conclusions:

• The introduced gridding and parameter expansion methods are effective for scalable spatial GP modeling on massive datasets.
• These techniques enhance computational efficiency and statistical performance of MCMC algorithms in spatial statistics.
• The methods are validated through extensive simulations and a forestry application using NASA G-LiHT remotely sensed data.