Eddington's Demon: Inferring Galaxy Mass Functions and other Distributions from Uncertain Data

TL;DR

This paper introduces a fast, flexible modified maximum likelihood method for accurately inferring galaxy mass functions from uncertain, biased data, outperforming traditional Bayesian approaches in speed and ease of use.

Contribution

The paper presents a novel, computationally efficient MML estimator that handles observational uncertainties, biases, and complex selection effects in galaxy mass function inference, extending to multi-dimensional distributions.

Findings

Accurately recovers galaxy mass functions from uncertain data.

Demonstrates the method's speed and robustness with mock surveys.

Provides a versatile tool applicable to various astronomical distributions.

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 multi-dimensional 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 emphasise the necessity of accounting for observational uncertainties in MFs of modern galaxy surveys.