Valid Model-Free Spatial Prediction
Open accessAbstract
Predicting the response at an unobserved location is a fundamental problem in spatial statistics. Given the difficulty in modeling spatial dependence, especially in non-stationary cases, model-based prediction intervals are at risk of misspecification bias that can negatively affect their validity. Here we present a new approach for model-free nonparametric spatial prediction based on the conformal prediction machinery. Our key observation is that spatial data can be treated as exactly or approximately exchangeable in a wide range of settings. In particular, under an infill asymptotic regime, we prove that the response values are, in a certain sense, locally approximately exchangeable for a broad class of spatial processes, and we develop a local spatial conformal prediction algorithm that yields valid prediction intervals without strong model assumptions like stationarity. Numerical examples with both real and simulated data confirm that the proposed conformal prediction intervals are valid and generally more efficient than existing model-based procedures for large datasets across a range of non-stationary and non-Gaussian settings.
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At worst, there is weak dependence such that conformal prediction inference is only asymptotically valid.
“At worst, there is weak dependence such that conformal prediction inference is only asymptotically valid.”
From Forecasting Extreme Temperatures in Siberia Using Supervised Learning and Conformal Prediction Regions (2025) · cites this paper as Mao et al., 2022
The Introduction and Theorem 2 in ‘Theoretical validity of LSCP’ support asymptotic validity for local spatial conformal prediction at a fixed location under specified conditions. They do not characterize those conditions as ‘weak dependence.’ The paper also establishes finite-sample marginal validity for its global method when locations are randomly sampled, so ‘only asymptotically valid’ does not apply to its conformal methods generally. Page numbers are unavailable in our copy. (LLM, conf=0.86)
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- Authors
- Mao, H., Martin, R., & Reich, B. J.
- Affiliations
- Statistical and Applied Mathematical Sciences Institute (US)
- North Carolina State University (US)
- Corresponding author
- Reich, Brian J.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2023-01-05
- Volume
- 119
- Issue
- 546
- Pages
- 904-914
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- PMC
- PMC11262549
- OpenAlex
- W4287750851
- Cited by
- 28
- References
- 39
- Citations by year
- 2026: 8 · 2025: 12 · 2024: 2 · 2023: 4 · 2022: 1 · 2020: 1
- FWCI
- 3.82
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Journal of the American Statistical Association (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- arXiv (Cornell University) (cc-by)
- Funders
- National Institutes of Health (DMS–1638521, DMS–1811802, (R01ES031651, R01ES027892)
- King Abdullah University of Science and Technology ((R01ES031651, R01ES027892, 3800.2)
- Topics
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
- Physical Sciences › Mathematics › Applied Mathematics › Point processes and geometric inequalities
- Physical Sciences › Computer Science › Artificial Intelligence › Gaussian Processes and Bayesian Inference
- Keywords
- conformal prediction, prediction intervals, exchangeability, infill asymptotics, model misspecification, spatial statistics
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