Valid Model-Free Spatial Prediction

Huiying Mao, Ryan Martin, Brian J. J. Reich

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Predicting the response at an unobserved location is afundamental problem in spatial statistics. Giventhe difficulty in modeling spatial dependence, especially in nonstationary cases, model-based predictionintervals are at risk of misspecification bias that can negatively affect their validity. Here we present a newapproach for model-free nonparametric spatial prediction based on theconformal predictionmachinery.Our key observation is that spatial data can be treated as exactly or approximately exchangeable in awide range of settings. In particular, under an infill asymptotic regime, we prove that the response valuesare, in a certain sense, locally approximately exchangeable for a broad class of spatial processes, and wedevelop a local spatial conformal prediction algorithm that yields valid prediction intervals without strongmodel assumptions like stationarity. Numerical exampleswith both real and simulated data confirm that theproposed conformal prediction intervals are valid and generally more efficient than existing model-basedprocedures for large datasets across a rangeof nonstationary and non-Gaussian settings.
Original languageEnglish (US)
Pages (from-to)1-11
Number of pages11
JournalJournal of the American Statistical Association
StatePublished - Jan 5 2023
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2023-01-24
Acknowledged KAUST grant number(s): 3800.2
Acknowledgements: HM (DMS–1638521) and RM (DMS–1811802) are supported by the National Science Foundation. BJR is supported by the National Institutes of Health (R01ES031651 and R01ES027892) and King Abdullah University of Science and Technology (3800.2).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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