Multitaper spectral estimation for spatial point processes (multitaper_spp)

Overview

multitaper_spp provides the Python implementation of the estimators used in

Mastrilli (2025), Minimax estimation of the structure factor of spatial point processes

This repository includes:

• The implementation of a multitaper estimator, with a local cross-validation procedure to select the number of tapers.
• The implementation of a kernel estimator, with a cross-validation procedure to select the bandwidth, following Yang & Guan (2024) and Ding et al. (2025).
• Scripts to reproduce all figures from the paper Mastrilli (2025)

Dependencies

• Compatible with .
• Requires the Python package numba.
• The script pps.py interfaces with the R package spatstat for simulating DPP and LGCP point processes.

Contents

• tutorial.py — Quick-start example demonstrating how to estimate the structure factor of Ginibre, Thomas, and perturbed lattice point processes using both multitaper and kernel estimators.

• pp_generation/ — Functions for simulating spatial point processes, including Thomas, Matérn cluster, LGCP, Ginibre, perturbed lattice, and Bessel DPP models.

• spectral_estimators/ — Core routines for computing multitaper and kernel estimators of the structure factor.

• companion_paper/ — Scripts used to generate the data for Figure 1 of the companion research paper Mastrilli (2025)

How to cite

@preprint{mastrilli25mt,
  title   = {Minimax estimation of the structure factor of spatial point processes},
  author  = {Mastrilli, Gabriel},
  year    = {2025},
  journal = {arXiv},
  arxivid = {},
}

References

• Junho Yang and Yongtao Guan.
  Fourier analysis of spatial point processes.
  arXiv preprint arXiv:2401.06403, 2024.

• Qi-Wen Ding, Junho Yang, and Joonho Shin.
  Pseudo-spectra of multivariate inhomogeneous spatial point processes.
  arXiv preprint arXiv:2502.09948, 2025.