Remote sensing data have been widely used to study various geophysical processes. With the advances in remote sensing technology, massive amount of remote sensing data are collected in space over time. Different satellite instruments typically have different footprints, measurement‐error characteristics, and data coverages. To combine data sets from different satellite instruments, we propose a dynamic fused Gaussian process (DFGP) model that enables fast statistical inference such as filtering and smoothing for massive spatio‐temporal data sets in a data‐fusion context. Based upon a spatio‐temporal‐random‐effect model, the DFGP methodology represents the underlying true process with two components: a linear combination of a small number of basis functions and random coefficients with a general covariance matrix, together with a linear combination of a large number of basis functions and Markov random coefficients. To model the underlying geophysical process at different spatial resolutions, we rely on the change‐of‐support property, which also allows efficient computations in the DFGP model. To estimate model parameters, we devise a computationally efficient stochastic expectation‐maximization algorithm to ensure its scalability for massive data sets. The DFGP model is applied to a total of 3.7 million sea surface temperature data sets in the tropical Pacific Ocean for a one‐week time period in 2010 from Moderate Resolution Imaging Spectroradiometer (MODIS) and Advanced Microwave Scanning Radiometer‐Earth Observing System (AMSR‐E) instruments.
The log‐Gaussian Cox process is a flexible and popular stochastic process for modeling point patterns exhibiting spatial and space‐time dependence. Model fitting requires approximation of stochastic integrals which is implemented through discretization over the domain of interest. With fine scale discretization, inference based on Markov chain Monte Carlo is computationally burdensome because of the cost of matrix decompositions and storage, such as the Cholesky, for high dimensional covariance matrices associated with latent Gaussian variables. This article addresses these computational bottlenecks by combining two recent developments: (i) a data augmentation strategy that has been proposed for space‐time Gaussian Cox processes that is based on exact Bayesian inference and does not require fine grid approximations for infinite dimensional integrals, and (ii) a recently developed family of sparsity‐inducing Gaussian processes, called nearest‐neighbor Gaussian processes, to avoid expensive matrix computations. Our inference is delivered within the fully model‐based Bayesian paradigm and does not sacrifice the richness of traditional log‐Gaussian Cox processes. We apply our method to crime event data in San Francisco and investigate the recovery of the intensity surface.
more » « less- Award ID(s):
- 1916349
- NSF-PAR ID:
- 10091086
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Journal of Time Series Analysis
- Volume:
- 40
- Issue:
- 3
- ISSN:
- 0143-9782
- Page Range / eLocation ID:
- p. 269-287
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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