Eddington's demon: Inferring galaxy mass functions and other distributions from uncertain data
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...
| Main Authors: | , , , |
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| Format: | Journal Article |
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Oxford University Press
2018
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| Online Access: | http://hdl.handle.net/20.500.11937/68228 |
| _version_ | 1848761777032003584 |
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| author | Obreschkow, D. Murray, Steven Robotham, A. Westmeier, T. |
| author_facet | Obreschkow, D. Murray, Steven Robotham, A. Westmeier, T. |
| author_sort | Obreschkow, D. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T10:37:03Z |
| format | Journal Article |
| id | curtin-20.500.11937-68228 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:37:03Z |
| publishDate | 2018 |
| publisher | Oxford University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-682282018-09-26T06:20:31Z Eddington's demon: Inferring galaxy mass functions and other distributions from uncertain data Obreschkow, D. Murray, Steven Robotham, A. Westmeier, T. 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. 2018 Journal Article http://hdl.handle.net/20.500.11937/68228 10.1093/mnras/stx3155 Oxford University Press fulltext |
| spellingShingle | Obreschkow, D. Murray, Steven Robotham, A. Westmeier, T. Eddington's demon: Inferring galaxy mass functions and other distributions from uncertain data |
| title | Eddington's demon: Inferring galaxy mass functions and other distributions from uncertain data |
| title_full | Eddington's demon: Inferring galaxy mass functions and other distributions from uncertain data |
| title_fullStr | Eddington's demon: Inferring galaxy mass functions and other distributions from uncertain data |
| title_full_unstemmed | Eddington's demon: Inferring galaxy mass functions and other distributions from uncertain data |
| title_short | Eddington's demon: Inferring galaxy mass functions and other distributions from uncertain data |
| title_sort | eddington's demon: inferring galaxy mass functions and other distributions from uncertain data |
| url | http://hdl.handle.net/20.500.11937/68228 |