kendall

Calculate non-parametric correlation coefficient Kendall's tau, accounting for censoring (upper/lower limits), based on the two-variable correlation formalism of Akrita & Siebert. 1996. MNRAS 278, 919-924. Additional function is included to determine the sensitivity of the correlation coefficient to individual datum (done by bootstrapping) and/or uncertainties in the data (done by Monte Carlo sampling).

While this code is provided publicly, I request that any use thereof be cited in any publications in which this code is used. For this purpose, the zenodo DOI is listed below as well as a BibTeX reference. This script was initially developed, implemented, and tested for work presented in Flury et al. 2022 ApJ 930, 126.

Example Usage

``` python from kendall import *

gen random data

np.random.seed(123) x = np.random.rand(89) y = x+0.1*np.random.randn(len(x))

gen random "upper limits"

censors = np.ones((2,len(x))) uplims = np.unique(np.random.randint(0,high=len(x)-1,size=60)) censors[1,uplims]=0 uncens = [i for i in range(len(x)) if i not in uplims]

faux uncertainties, accounting for upper limits

xerr = 0.1np.random.rand(len(x))censors[0] yerr = 0.1np.random.rand(len(y))censors[1]

Kendall tau

tau,p = kendall(x,y,censors=censors) taulo,tauup = tauconf(x,y,censors,method='bootstrap') print(f'censored Kendall tau: {tau:.3f}-{taulo:.3f}+{tau_up:.3f}, p: {p:.3e}') which prints the following to the command line censored Kendall tau: 0.465-0.018+0.018, p: 1.094e-10 ```

BibTeX Reference

bibtex @SOFTWARE{Flury_kendall, author = {{Flury}, Sophia R.}, title = "{kendall}", year = 2023, month = aug, version = {1.0.0}, url = {https://github.com/sflury/kendall}, doi = {10.5281/zenodo.14732912} }

Zenodo DOI badge:

Flury et al. 2022 ApJ 930, 126.

bibtex @ARTICLE{2022ApJ...930..126F, author = {{Flury}, Sophia R. and {Jaskot}, Anne E. and {Ferguson}, Harry C. and {Worseck}, G{\'a}bor and {Makan}, Kirill and {Chisholm}, John and {Saldana-Lopez}, Alberto and {Schaerer}, Daniel and {McCandliss}, Stephan R. and {Xu}, Xinfeng and {Wang}, Bingjie and {Oey}, M.~S. and {Ford}, N.~M. and {Heckman}, Timothy and {Ji}, Zhiyuan and {Giavalisco}, Mauro and {Amor{\'\i}n}, Ricardo and {Atek}, Hakim and {Blaizot}, Jeremy and {Borthakur}, Sanchayeeta and {Carr}, Cody and {Castellano}, Marco and {De Barros}, Stephane and {Dickinson}, Mark and {Finkelstein}, Steven L. and {Fleming}, Brian and {Fontanot}, Fabio and {Garel}, Thibault and {Grazian}, Andrea and {Hayes}, Matthew and {Henry}, Alaina and {Mauerhofer}, Valentin and {Micheva}, Genoveva and {Ostlin}, Goran and {Papovich}, Casey and {Pentericci}, Laura and {Ravindranath}, Swara and {Rosdahl}, Joakim and {Rutkowski}, Michael and {Santini}, Paola and {Scarlata}, Claudia and {Teplitz}, Harry and {Thuan}, Trinh and {Trebitsch}, Maxime and {Vanzella}, Eros and {Verhamme}, Anne}, title = "{The Low-redshift Lyman Continuum Survey. II. New Insights into LyC Diagnostics}", journal = {\apj}, keywords = {Reionization, Galactic and extragalactic astronomy, Hubble Space Telescope, Ultraviolet astronomy, Emission line galaxies, 1383, 563, 761, 1736, 459, Astrophysics - Astrophysics of Galaxies, Astrophysics - Cosmology and Nongalactic Astrophysics}, year = 2022, month = may, volume = {930}, number = {2}, eid = {126}, pages = {126}, doi = {10.3847/1538-4357/ac61e4}, archivePrefix = {arXiv}, eprint = {2203.15649}, primaryClass = {astro-ph.GA}, adsurl = {https://ui.adsabs.harvard.edu/abs/2022ApJ...930..126F}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} }

Akritas & Seibert 1996

bibtex @ARTICLE{1996MNRAS.278..919A, author = {{Akritas}, M.~G. and {Siebert}, J.}, title = "{A test for partial correlation with censored astronomical data}", journal = {\mnras}, keywords = {METHODS: STATISTICAL, GALAXIES: ACTIVE, X-RAYS: GALAXIES, Astrophysics}, year = 1996, month = feb, volume = {278}, number = {4}, pages = {919-924}, doi = {10.1093/mnras/278.4.919}, archivePrefix = {arXiv}, eprint = {astro-ph/9508018}, primaryClass = {astro-ph}, adsurl = {https://ui.adsabs.harvard.edu/abs/1996MNRAS.278..919A}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} }

Licensing

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see https://www.gnu.org/licenses/.