This repository contains the reference implementation of the method described in "Lipschitz-Driven Inference: Bias-corrected Confidence Intervals for Spatial Linear Models" by David R. Burt, Renato Berlinghieri, Stephen Bates, and Tamara Broderick. Code was run in python3.12.

Citation

@misc{burt2025lipschitz_driven_inference,
      title={Lipschitz-Driven Inference: Bias-corrected Confidence Intervals for Spatial Linear Models}, 
      author={David R. Burt and Renato Berlinghieri and Stephen Bates and Tamara Broderick},
      year={2025},
      eprint={2502.06067},
      archivePrefix={arXiv},
      primaryClass={stat.ML},
      url={https://arxiv.org/abs/2502.06067}, 
}

To install, run pip install . from the root directory; dependencies are included in the setup.py file and should be installed automatically.

Navigate to the directory Lipschitz-Driven-Inference/experiments/simulations. To recreate experiments with the same settings as the paper, run bash run.sh. Results will be saved in Lipschitz-Driven-Inference/experiments/simulations/results.

Navigate to the directory Lipschitz-Driven-Inference/experiments/real_data. To recreate experiments with the same settings as the paper, run bash run.sh. Results will be saved in Lipschitz-Driven-Inference/experiments/real_data/results.

Data is downloaded from the Dropbox link provided in the readme of https://github.com/Earth-Intelligence-Lab/uncertainty-quantification. Relevant citations for using the real data:

Lu, K., Bates, S., and Wang, S. (2024). Quantifying uncertainty in area and regression coefficient estimation from remote sensing maps. arXiv preprint arXiv:2407.13659.

USFS (2023). USFS tree canopy cover v2021.4 (Conterminous United States and Southeastern Alaska).

Trabucco, A. (2019). Global aridity index and potential evapotranspiration (ET0) climate database v2. CGIAR Consortium for Spatial Information.

NASA Jet Propulsion Lab (2020). NASADEM merged DEM global 1 arc second v001 [data set]. NASA EOSDIS Land Processes DAAC.