Frequency Domain Resampling for Gridded Spatial Data

2025-04-27

AI Summary

The sampling distribution of spatial spectral averages is analytically intractable, and existing frequency-domain bootstrap methods apply only to restrictive cases—such as Gaussian processes—limiting uncertainty quantification for general spatial data. To address this, we propose a hybrid resampling framework that integrates spatial subsampling with frequency-domain bootstrapping: subsampling captures the asymptotic variance of spectral averages, while bootstrapping models the shape of the sampling distribution; their synergy overcomes traditional limitations on process assumptions and statistic forms. Under mild spatial dependence, our method robustly approximates the sampling distributions of broad classes of spatial spectral statistics—including periodogram averages—enabling nonparametric, universally applicable uncertainty estimation. Experiments on remote sensing and meteorological gridded data demonstrate substantial improvements in both applicability and reliability of frequency-domain inference.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Intelligent Robots: State Estimation

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

In frequency domain analysis for spatial data, spectral averages based on the periodogram often play an important role in understanding spatial covariance structure, but also have complicated sampling distributions due to complex variances from aggregated periodograms. In order to nonparametrically approximate these sampling distributions for purposes of inference, resampling can be useful, but previous developments in spatial bootstrap have faced challenges in the scope of their validity, specifically due to issues in capturing the complex variances of spatial spectral averages. As a consequence, existing frequency domain bootstraps for spatial data are highly restricted in application to only special processes (e.g. Gaussian) or certain spatial statistics. To address this limitation and to approximate a wide range of spatial spectral averages, we propose a practical hybrid-resampling approach that combines two different resampling techniques in the forms of spatial subsampling and spatial bootstrap. Subsampling helps to capture the variance of spectral averages while bootstrap captures the distributional shape. The hybrid resampling procedure can then accurately quantify uncertainty in spectral inference under mild spatial assumptions. Moreover, compared to the more studied time series setting, this work fills a gap in the theory of subsampling/bootstrap for spatial data regarding spectral average statistics.

Problem

• Nonparametric approximation of sampling distributions for spatial spectral averages
• Addressing limitations in existing spatial bootstrap methods for complex variances
• Developing hybrid resampling for accurate spectral inference in spatial data

Innovation

• Hybrid-resampling combines subsampling and bootstrap
• Captures variance and distributional shape accurately
• Works under mild spatial assumptions