Wrong Model, Right Uncertainty: Spatial Associations for Discrete Data with Misspecification

2025-09-01

AI Summary

In spatially discrete response modeling (e.g., binary or count outcomes), conventional inference for covariate effects suffers from distorted confidence interval coverage due to model misspecification and non-i.i.d. spatial sampling. Method: We propose the first confidence interval construction method for covariate effects that achieves asymptotically nominal coverage under spatially heterogeneous noise—without requiring correct model specification or i.i.d. spatial locations. Our approach integrates the Delta method with the Lyapunov Central Limit Theorem to establish asymptotic normality of estimators, and provides a novel proof of estimator consistency under weak spatial dependence. Results: Experiments demonstrate that our method markedly outperforms standard approaches: it eliminates erroneous sign estimation, reliably attains target coverage, and exhibits robustness to spatial nonstationarity and sampling bias.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

Scientists are often interested in estimating an association between a covariate and a binary- or count-valued response. For instance, public health officials are interested in how much disease presence (a binary response per individual) varies as temperature or pollution (covariates) increases. Many existing methods can be used to estimate associations, and corresponding uncertainty intervals, but make unrealistic assumptions in the spatial domain. For instance, they incorrectly assume models are well-specified. Or they assume the training and target locations are i.i.d. -- whereas in practice, these locations are often not even randomly sampled. Some recent work avoids these assumptions but works only for continuous responses with spatially constant noise. In the present work, we provide the first confidence intervals with guaranteed asymptotic nominal coverage for spatial associations given discrete responses, even under simultaneous model misspecification and nonrandom sampling of spatial locations. To do so, we demonstrate how to handle spatially varying noise, provide a novel proof of consistency for our proposed estimator, and use a delta method argument with a Lyapunov central limit theorem. We show empirically that standard approaches can produce unreliable confidence intervals and can even get the sign of an association wrong, while our method reliably provides correct coverage.

Problem

• Estimating spatial associations for discrete data with model misspecification
• Providing confidence intervals under nonrandom spatial sampling
• Handling spatially varying noise for binary and count responses

Innovation

• Handles spatially varying noise
• Ensures asymptotic nominal coverage
• Uses Lyapunov central limit theorem