@article{corner,
  doi = {10.21105/joss.00024},
  url = {https://doi.org/10.21105/joss.00024},
  year  = {2016},
  month = {jun},
  publisher = {The Open Journal},
  volume = {1},
  number = {2},
  pages = {24},
  author = {Daniel Foreman-Mackey},
  title = {corner.py: Scatterplot matrices in Python},
  journal = {The Journal of Open Source Software}
}
@article{dynesty,
abstract = {We present dynesty, a public, open-source, python package to estimate Bayesian posteriors and evidences (marginal likelihoods) using the dynamic nested sampling methods developed by Higson et al. By adaptively allocating samples based on posterior structure, dynamic nested sampling has the benefits of Markov chain Monte Carlo (MCMC) algorithms that focus exclusively on posterior estimation while retaining nested sampling's ability to estimate evidences and sample from complex, multimodal distributions. We provide an overview of nested sampling, its extension to dynamic nested sampling, the algorithmic challenges involved, and the various approaches taken to solve them in this and previous work. We then examine dynesty's performance on a variety of toy problems along with several astronomical applications. We find in particular problems dynesty can provide substantial improvements in sampling efficiency compared to popular MCMC approaches in the astronomical literature. More detailed statistical results related to nested sampling are also included in the appendix.},
archivePrefix = {arXiv},
arxivId = {1904.02180},
author = {Speagle, Joshua S},
doi = {10.1093/mnras/staa278},
eprint = {1904.02180},
file = {:home/jammy/Documents/Papers/PPLs/Dynesty.pdf:pdf},
issn = {0035-8711},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {data analysis,methods,statistical},
number = {3},
pages = {3132--3158},
title = {{dynesty: a dynamic nested sampling package for estimating Bayesian posteriors and evidences}},
volume = {493},
year = {2020}
}
@article{emcee,
abstract = {We introduce a stable, well tested Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman {\&} Weare (2010). The code is open source and has already been used in several published projects in the astrophysics literature. The algorithm behind emcee has several advantages over traditional MCMC sampling methods and it has excellent performance as measured by the autocorrelation time (or function calls per independent sample). One major advantage of the algorithm is that it requires hand-tuning of only 1 or 2 parameters compared to {\$}\backslashsim N{\^{}}2{\$} for a traditional algorithm in an N-dimensional parameter space. In this document, we describe the algorithm and the details of our implementation and API. Exploiting the parallelism of the ensemble method, emcee permits any user to take advantage of multiple CPU cores without extra effort. The code is available online at http://dan.iel.fm/emcee under the MIT License.},
archivePrefix = {arXiv},
arxivId = {1202.3665},
author = {Foreman-Mackey, Daniel and Hogg, David W. and Lang, Dustin and Goodman, Jonathan},
doi = {10.1086/670067},
eprint = {1202.3665},
file = {:home/jammy/Documents/Papers/PPLs/Emcee.pdf:pdf},
issn = {00046280},
journal = {Publications of the Astronomical Society of the Pacific},
number = {925},
pages = {306--312},
title = {{emcee : The MCMC Hammer }},
volume = {125},
year = {2013}
}
@article{matplotlib,
  Author    = {Hunter, J. D.},
  Title     = {Matplotlib: A 2D graphics environment},
  Journal   = {Computing in Science \& Engineering},
  Volume    = {9},
  Number    = {3},
  Pages     = {90--95},
  abstract  = {Matplotlib is a 2D graphics package used for Python for
  application development, interactive scripting, and publication-quality
  image generation across user interfaces and operating systems.},
  publisher = {IEEE COMPUTER SOC},
  doi       = {10.1109/MCSE.2007.55},
  year      = 2007
}
@article{multinest,
abstract = {We present further development and the first public release of our multimodal nested sampling algorithm, called MultiNest. This Bayesian inference tool calculates the evidence, with an associated error estimate, and produces posterior samples from distributions that may contain multiple modes and pronounced (curving) degeneracies in high dimensions. The developments presented here lead to further substantial improvements in sampling efficiency and robustness, as compared to the original algorithm presented in Feroz and Hobson, which itself significantly outperformed existing Markov chain Monte Carlo techniques in a wide range of astrophysical inference problems. The accuracy and economy of the MultiNest algorithm are demonstrated by application to two toy problems and to a cosmological inference problem focusing on the extension of the vanilla $\Lambda$ cold dark matter model to include spatial curvature and a varying equation of state for dark energy. The MultiNest software, which is fully parallelized using MPI and includes an interface to CosmoMC, is available at http://www.mrao.cam.ac.uk/software/multinest/. It will also be released as part of the SuperBayeS package, for the analysis of supersymmetric theories of particle physics, at http://www.superbayes.org. {\textcopyright} 2009 RAS.},
archivePrefix = {arXiv},
arxivId = {0809.3437},
author = {Feroz, F. and Hobson, M. P. and Bridges, M.},
doi = {10.1111/j.1365-2966.2009.14548.x},
eprint = {0809.3437},
isbn = {0035-8711},
issn = {00358711},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Methods: Data analysis,Methods: Statistical},
number = {4},
pages = {1601--1614},
pmid = {29176},
title = {{MultiNest: An efficient and robust Bayesian inference tool for cosmology and particle physics}},
volume = {398},
year = {2009}
}
@ARTICLE{numpy,
  author={S. {van der Walt} and S. C. {Colbert} and G. {Varoquaux}},
  doi={10.1109/MCSE.2011.37},
  journal={Computing in Science Engineering},
  title={The NumPy Array2D: A Structure for Efficient Numerical Computation},
  year={2011},
  volume={13},
  number={2},
  pages={22-30}}
@article{pymultinest,
abstract = {Context. Aims. Active galactic nuclei are known to have complex X-ray spectra that depend on both the properties of the accreting super-massive black hole (e.g. mass, accretion rate) and the distribution of obscuring material in its vicinity (i.e. the "torus"). Often however, simple and even unphysical models are adopted to represent the X-ray spectra of AGN, which do not capture the complexity and diversity of the observations. In the case of blank field surveys in particular, this should have an impact on e.g. the determination of the AGN luminosity function, the inferred accretion history of the Universe and also on our understanding of the relation between AGN and their host galaxies. Methods. We develop a Bayesian framework for model comparison and parameter estimation of X-ray spectra. We take into account uncertainties associated with both the Poisson nature of X-ray data and the determination of source redshift using photometric methods. We also demonstrate how Bayesian model comparison can be used to select among ten different physically motivated X-ray spectral models the one that provides a better representation of the observations. This methodology is applied to X-ray AGN in the 4 Ms Chandra Deep Field South. Results. For the {\~{}}350 AGN in that field, our analysis identifies four components needed to represent the diversity of the observed X-ray spectra: (1) an intrinsic power law; (2) a cold obscurer which reprocesses the radiation due to photo-electric absorption, Compton scattering and Fe-K fluorescence; (3) an unabsorbed power law associated with Thomson scattering off ionised clouds; and (4) Compton reflection, most noticeable from a stronger-than-expected Fe-K line. Simpler models, such as a photo-electrically absorbed power law with a Thomson scattering component, are ruled out with decisive evidence (B {\textgreater} 100). We also find that ignoring the Thomson scattering component results in underestimation of the inferred column density, NH, of the obscurer. Regarding the geometry of the obscurer, there is strong evidence against both a completely closed (e.g. sphere), or entirely open (e.g. blob of material along the line of sight), toroidal geometry in favour of an intermediate case. Conclusions. Despite the use of low-count spectra, our methodology is able to draw strong inferences on the geometry of the torus. Simpler models are ruled out in favour of a geometrically extended structure with significant Compton scattering. We confirm the presence of a soft component, possibly associated with Thomson scattering off ionised clouds in the opening angle of the torus. The additional Compton reflection required by data over that predicted by toroidal geometry models, may be a sign of a density gradient in the torus or reflection off the accretion disk. Finally, we release a catalogue of AGN in the CDFS with estimated parameters such as the accretion luminosity in the 2-10 keV band and the column density, NH, of the obscurer. {\textcopyright} ESO, 2014.},
archivePrefix = {arXiv},
arxivId = {1402.0004},
author = {Buchner, J. and Georgakakis, A. and Nandra, K. and Hsu, L. and Rangel, C. and Brightman, M. and Merloni, A. and Salvato, M. and Donley, J. and Kocevski, D.},
doi = {10.1051/0004-6361/201322971},
eprint = {1402.0004},
file = {:home/jammy/Documents/Papers/Stats/ButchnerPyMultiNest.pdf:pdf},
issn = {14320746},
journal = {Astronomy and Astrophysics},
keywords = {Accretion, accretion disks,Galaxies: high-redshift,Galaxies: nuclei,Methods: data analysis,Methods: statistical,X-rays: galaxies},
pages = {A125},
title = {{X-ray spectral modelling of the AGN obscuring region in the CDFS: Bayesian model selection and catalogue}},
volume = {564},
year = {2014}
}
@misc{pyautofit,
  author = {James Nightingale and Richard Hayes},
  title = {PyAutoFit: A classy Probabilistic Programming Language for Complex Model-fitting},
  year = {2020},
  publisher = {​GitHub},
  journal = {​GitHub repository},
  url = {https://github.com/rhayes777/PyAutoFit}
}
@article{pyswarms,
    author  = {Lester James V. Miranda},
    title   = "{P}y{S}warms, a research-toolkit for {P}article {S}warm {O}ptimization in {P}ython",
    journal = {Journal of Open Source Software},
    year    = {2018},
    volume  = {3},
    issue   = {21},
    doi     = {10.21105/joss.00433},
    url     = {https://doi.org/10.21105/joss.00433}
}
@book{python,
 author = {Van Rossum, Guido and Drake, Fred L.},
 title = {Python 3 Reference Manual},
 year = {2009},
 isbn = {1441412697},
 publisher = {CreateSpace},
 address = {Scotts Valley, CA}
}
@article{scipy,
       author = {{Virtanen}, Pauli and {Gommers}, Ralf and {Oliphant},
         Travis E. and {Haberland}, Matt and {Reddy}, Tyler and
         {Cournapeau}, David and {Burovski}, Evgeni and {Peterson}, Pearu
         and {Weckesser}, Warren and {Bright}, Jonathan and {van der Walt},
         St{\'e}fan J.  and {Brett}, Matthew and {Wilson}, Joshua and
         {Jarrod Millman}, K.  and {Mayorov}, Nikolay and {Nelson}, Andrew
         R.~J. and {Jones}, Eric and {Kern}, Robert and {Larson}, Eric and
         {Carey}, CJ and {Polat}, {\.I}lhan and {Feng}, Yu and {Moore},
         Eric W. and {Vand erPlas}, Jake and {Laxalde}, Denis and
         {Perktold}, Josef and {Cimrman}, Robert and {Henriksen}, Ian and
         {Quintero}, E.~A. and {Harris}, Charles R and {Archibald}, Anne M.
         and {Ribeiro}, Ant{\^o}nio H. and {Pedregosa}, Fabian and
         {van Mulbregt}, Paul and {Contributors}, SciPy 1. 0},
        title = "{SciPy 1.0: Fundamental Algorithms for Scientific
                  Computing in Python}",
      journal = {Nature Methods},
      year = "2020",
      volume={17},
      pages={261--272},
      adsurl = {https://rdcu.be/b08Wh},
      doi = {10.1038/s41592-019-0686-2},
}