Advection-aligned block Vecchia inference for spatio-temporal Gaussian processes
Abstract
Vecchia approximations enable scalable likelihood-based inference for large Gaussian process models, but their accuracy depends on the choice of conditioning sets. For spatio-temporal processes with advection, target-centered conditioning can omit informative past observations. Motivated by total column ozone observations from the Geostationary Environment Monitoring Spectrometer (GEMS), we propose a data-driven, advection-aligned block Vecchia approximation that incorporates estimated transport direction into temporal conditioning geometry. Observation locations need not lie on a regular grid. An initial advection vector is estimated from the data and used once to select transport-aligned past-time conditioning blocks. The resulting graph is held fixed during optimization, while covariance and advection parameters remain free to vary. This separates neighbor selection from covariance estimation, avoids repeated parameter-dependent neighbor searches, and provides an interpretable connection between conditioning geometry and estimated transport. Batched graphics processing unit (GPU) operations evaluate the likelihood and its gradients. In a matched comparison of daily GEMS datasets from July 2024 and July 2025, advection-aligned conditioning attained a lower fitted Vecchia negative log-likelihood than target-centered conditioning on 53 of 61 days. In six Matérn simulation scenarios with 120 matched eight-hour fields each, advection-aligned conditioning reduced advection-vector root mean squared error relative to target-centered conditioning at the same conditioning-block budget, with the largest reduction under strong transport.
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BibTeX
@misc{lee2026advectionaligned,
title = {{Advection-aligned block Vecchia inference for spatio-temporal Gaussian processes}},
author = {Joonwon Lee and Michael L. Stein},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08938},
eprint = {2611.08938},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08938},
}
RIS
TY - UNPB
TI - Advection-aligned block Vecchia inference for spatio-temporal Gaussian processes
AU - Joonwon Lee
AU - Michael L. Stein
PY - 2026
DA - 2026/11/06
PB - arXiv
DO - 10.48550/arxiv.2611.08938
UR - https://arxiv.org/abs/2611.08938
AB - Vecchia approximations enable scalable likelihood-based inference for large Gaussian process models, but their accuracy depends on the choice of conditioning sets. For spatio-temporal processes with advection, target-centered conditioning can omit informative past observations. Motivated by total column ozone observations from the Geostationary Environment Monitoring Spectrometer (GEMS), we propose a data-driven, advection-aligned block Vecchia approximation that incorporates estimated transport direction into temporal conditioning geometry. Observation locations need not lie on a regular grid. An initial advection vector is estimated from the data and used once to select transport-aligned past-time conditioning blocks. The resulting graph is held fixed during optimization, while covariance and advection parameters remain free to vary. This separates neighbor selection from covariance estimation, avoids repeated parameter-dependent neighbor searches, and provides an interpretable connection between conditioning geometry and estimated transport. Batched graphics processing unit (GPU) operations evaluate the likelihood and its gradients. In a matched comparison of daily GEMS datasets from July 2024 and July 2025, advection-aligned conditioning attained a lower fitted Vecchia negative log-likelihood than target-centered conditioning on 53 of 61 days. In six Matérn simulation scenarios with 120 matched eight-hour fields each, advection-aligned conditioning reduced advection-vector root mean squared error relative to target-centered conditioning at the same conditioning-block budget, with the largest reduction under strong transport.
ER -