Calibrated Bayesian inference for random fields on large irregular domains using the debiased spatial Whittle likelihood

2025-05-29

AI Summary

Bayesian inference for stationary random fields over large irregular spatial domains is computationally prohibitive with conventional methods, while existing Whittle likelihood approaches suffer from bias and inefficiency. This paper introduces the first debiased spatial Whittle likelihood integrated with composite likelihood correction, enabling quasi-linear $O(n log n)$ computation via FFT within a spectral-domain modeling framework. The proposed method substantially improves posterior calibration and ensures nominal coverage of high-posterior-density credible sets. Extensive experiments—including simulations and two real-world datasets—demonstrate its statistical reliability and computational efficiency: it achieves higher inference accuracy than standard Whittle methods and accelerates computation by several orders of magnitude relative to MCMC. The core contribution is a novel spectral-domain Bayesian inference paradigm that simultaneously guarantees theoretical consistency, high credible-set coverage accuracy, and scalability to large spatial datasets.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Bayesian inference for stationary random fields is computationally demanding. Whittle-type likelihoods in the frequency domain based on the fast Fourier Transform (FFT) have several appealing features: i) low computational complexity of only $mathcal{O}(n log n)$, where $n$ is the number of spatial locations, ii) robustness to assumptions of the data-generating process, iii) ability to handle missing data and irregularly spaced domains, and iv) flexibility in modelling the covariance function via the spectral density directly in the spectral domain. It is well known, however, that the Whittle likelihood suffers from bias and low efficiency for spatial data. The debiased Whittle likelihood is a recently proposed alternative with better frequentist properties. We propose a methodology for Bayesian inference for stationary random fields using the debiased spatial Whittle likelihood, with an adjustment from the composite likelihood literature. The adjustment is shown to give a well-calibrated Bayesian posterior as measured by coverage properties of credible sets, without sacrificing the quasi-linear computation time. We apply the method to simulated data and two real datasets.

Problem

• Bayesian inference for random fields is computationally demanding
• Whittle likelihood suffers from bias and low efficiency
• Debiased Whittle likelihood improves frequentist properties but needs calibration

Innovation

• Debiased spatial Whittle likelihood for Bayesian inference
• Composite likelihood adjustment for calibrated posteriors
• Quasi-linear computation time with FFT efficiency