Yue, S., Feng, L., Ju, W., Pan, J., Huang, Z., Fang, F., Li, Z., Cai, Y., & Zhu, W. (2024). Pair Counting without Binning - A New Approach to Correlation Functions in Clustering Statistics. Monthly Notices of the Royal Astronomical Society, 000, 1–17. Preprint retrieved from arXiv:2408.16398v2
This paper aims to address the computational challenges of estimating N-point correlation functions (NPCFs), particularly 2PCF and 3PCF, in large-scale cosmological datasets by developing a fast and efficient algorithm based on a novel "pair counting without binning" approach.
The authors propose a method that reinterprets the traditional pair/triplet counting in NPCF estimation as a counts-in-cells (CIC) operation. This allows them to leverage the Multi-Resolution Analysis for Cosmic Statistics (MRACS) scheme, which utilizes a set of basis functions to represent the density field and efficiently computes CIC statistics through convolutions. They introduce a generalized 2PCF definition that accommodates arbitrary window functions for binning, going beyond the limitations of traditional sharp-edged bins. For 3PCF, they propose a triple-sphere binning scheme that simplifies the computation and derive analytical expressions for binning corrections.
The "pair counting without binning" approach provides a novel and efficient way to estimate NPCFs, particularly 2PCF and 3PCF, in large cosmological datasets. The proposed algorithm offers significant speed improvements over traditional methods while enabling flexible binning schemes and accounting for binning effects in theoretical modeling. This approach is particularly valuable for analyzing the massive datasets from ongoing and upcoming surveys like Euclid, LSST, and DESI.
This research significantly contributes to the field of clustering analysis in cosmology by providing a fast and efficient algorithm for NPCF estimation. This is crucial for extracting cosmological information from the increasingly large and complex datasets generated by modern surveys, ultimately leading to more precise constraints on cosmological models and a deeper understanding of the Universe's large-scale structure.
While the paper focuses on 2PCF and 3PCF, extending this approach to higher-order correlation functions (NPCFs with N > 3) presents a potential avenue for future research. Further investigation into the optimal choice of window functions for specific scientific objectives and the development of efficient implementations for massively parallel architectures are also promising directions.
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by Shiyu Yue, L... at arxiv.org 11-06-2024
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