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Confidence regions for spatial excursion sets from repeated random field observations, with an application to
Max Sommerfeld1, Stephan Sain2, Armin Schwartzman3
1FBMS, Universität Göttingen.
Journal of the American Statistical Association
|August 28, 2019
Summary
This study provides confidence regions for spatial data analysis, helping to identify areas exceeding temperature thresholds. The novel method uses bootstrap techniques for reliable excursion set estimation.
Area of Science:
- Spatial statistics
- Statistical inference
- Environmental science
Background:
- Estimating excursion sets from noisy spatial data is challenging.
- Accurate confidence regions are crucial for understanding spatial phenomena above thresholds.
Purpose of the Study:
- To develop a method for constructing confidence regions for excursion sets of spatial functions.
- To apply this method to predict temperature changes in North America.
Main Methods:
- Utilizing asymptotically Gaussian estimators for spatial functions.
- Constructing data-dependent nested excursion sets as sub- and super-sets.
- Employing a multiplier bootstrap method for asymptotic coverage probabilities.
Main Results:
- The method provides reliable confidence regions for excursion sets.
- It does not require Gaussianity, stationarity, or smoothness assumptions.
- Identified regions in North America with projected temperature increases exceeding 2°C by mid-21st century.
Conclusions:
- The developed method offers a robust approach to excursion set estimation in spatial statistics.
- This technique has practical applications in climate change impact assessment and environmental monitoring.
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