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    Eddington's demon: Inferring galaxy mass functions and other distributions from uncertain data

    265622.pdf (7.332Mb)
    Access Status
    Open access
    Authors
    Obreschkow, D.
    Murray, Steven
    Robotham, A.
    Westmeier, T.
    Date
    2018
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Obreschkow, D. and Murray, S. and Robotham, A. and Westmeier, T. 2018. Eddington's demon: Inferring galaxy mass functions and other distributions from uncertain data. Monthly Notices of the Royal Astronomical Society. 474 (4): pp. 5500-5522.
    Source Title
    Monthly Notices of the Royal Astronomical Society
    DOI
    10.1093/mnras/stx3155
    ISSN
    0035-8711
    School
    Curtin Institute of Radio Astronomy (Physics)
    Remarks

    This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society ©: 2017 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.

    URI
    http://hdl.handle.net/20.500.11937/68228
    Collection
    • Curtin Research Publications
    Abstract

    We present a general modified maximum likelihood (MML) method for inferring generative distribution functions from uncertain and biased data. The MML estimator is identical to, but easier and many orders of magnitude faster to compute than the solution of the exact Bayesian hierarchical modelling of all measurement errors. As a key application, this method can accurately recover the mass function (MF) of galaxies, while simultaneously dealing with observational uncertainties (Eddington bias), complex selection functions and unknown cosmic large-scale structure. The MML method is free of binning and natively accounts for small number statistics and non-detections. Its fast implementation in the R-package dftools is equally applicable to other objects, such as haloes, groups, and clusters, as well as observables other than mass. The formalism readily extends to multidimensional distribution functions, e.g. a Choloniewski function for the galaxy mass-angular momentum distribution, also handled by dftools. The code provides uncertainties and covariances for the fitted model parameters and approximate Bayesian evidences. We use numerous mock surveys to illustrate and test the MML method, as well as to emphasize the necessity of accounting for observational uncertainties in MFs of modern galaxy surveys.

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