Valid model-free spatial prediction.

Area of Science:

• Spatial Statistics
• Geostatistics
• Machine Learning

Background:

• Spatial prediction is crucial but challenged by complex spatial dependence, particularly non-stationarity.
• Existing model-based prediction intervals risk misspecification bias, impacting validity.
• Nonparametric approaches are needed to overcome model limitations in spatial statistics.

Purpose of the Study:

• To develop a model-free, nonparametric spatial prediction method.
• To construct valid prediction intervals without assuming stationarity or specific spatial models.
• To enhance the reliability and efficiency of spatial prediction, especially for large datasets.

Main Methods:

• Utilizing conformal prediction machinery for spatial data.
• Leveraging the concept of local approximate exchangeability in spatial processes under infill asymptotics.
• Developing a local spatial conformal prediction algorithm.

Main Results:

• The proposed algorithm yields valid prediction intervals across various non-stationary and non-Gaussian settings.
• Conformal prediction intervals demonstrate improved efficiency compared to model-based methods for large datasets.
• The approach effectively handles spatial data without strong modeling assumptions.

Conclusions:

• The local spatial conformal prediction method offers a robust, model-free alternative for spatial prediction.
• This technique ensures prediction interval validity and enhances efficiency, particularly in complex spatial scenarios.
• The findings advance spatial statistics by providing reliable tools for prediction under uncertainty.