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

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
x_err = 0.1*np.random.rand(len(x))*censors[0]
y_err = 0.1*np.random.rand(len(y))*censors[1]
# Kendall tau
tau,p = kendall(x,y,censors=censors)
tau_lo,tau_up = tau_conf(x,y,censors,method='bootstrap')
print(f'censored Kendall tau: {tau:.3f}-{tau_lo:.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

@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.

@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

@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/.