Extracting distribution parameters from multiple uncertain observations with selection biases

By Ilya Mandel, W. Farr, Jonathan R. Gair. Monthly notices of the Royal Astronomical Society, 2018

372 citations recorded by the source corpus.

We derive a Bayesian framework for incorporating selection effects into population analyses. We allow for both measurement uncertainty in individual measurements and, crucially, for selection biases on the population of measurements, and show how to extract the parameters of the underlying distribution based on a set of observations sampled from this distribution. We illustrate the performance of this framework with an example from gravitational-wave astrophysics, demonstrating that the mass ratio distribution of merging compact-object binaries can be extracted from Malmquist-biased observations with substantial measurement uncertainty.

Subfields: Artificial Intelligence, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/598d63d46aa453b529a9c3147dac1fe31290d9b9

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Citations in the corpus

The effect of the metallicity-specific star formation history on double compact object mergers (2019, background): “…function), and do not reweigh by those priors; and we ignore the selection effects on the chirp mass for the purpose of population analysis, since the selection function does not vary significantly over the range of likelihood support (see Mandel et al. 2019 for a discussion of both issues).”
Observation of Gravitational Waves from the Coalescence of a 2.5–4.5 M ⊙ Compact Object and a Neutron Star (2024, methodology): “We employ hierarchical Bayesian inference to marginal-ize over the properties of individual events and infer the parameters of a given population model (e.g., Thrane & Talbot 2019; Mandel et al. 2019; Vitale et al. 2020).”
4-OGC: Catalog of Gravitational Waves from Compact Binary Mergers (2021, methodology): “…described by hyper-parameter Θpop, the population likelihood function can be described by inhomogeneous Poisson processes given as (Loredo 2004; Mandel et al. 2019; Thrane & Talbot 2020; Abbott et al. 2021h) ({ } ∣ ) ( ∣ ) ( ∣ ) ( )ò q p q q Q µ Q= d N N N e d d , , , 3N N i N i det pop…”
Hierarchical analysis of gravitational-wave measurements of binary black hole spin–orbit misalignments (2017, methodology): “These must be incorporated in the analysis to correctly infer the intrinsic subpopulation fractions (Farr et al. 2015; Mandel et al. 2016), but the impact is not expected to be significant in this case.”
Constraints from Gravitational-wave Detections of Binary Black Hole Mergers on the 12C(α, γ)16O Rate (2020, methodology): “We then perform a hierarchical Bayesian analysis (Mandel 2010; Mandel et al. 2019) on each set of 50 detections to recover the posterior over the population parameters, α, Mmax, β, and Mmin.”
A Future Percent-level Measurement of the Hubble Expansion at Redshift 0.8 with Advanced LIGO (2019, methodology): “We fit a parameterized model of the true mass distribution to this data set accounting for measurement error and selection effects in a hierarchical analysis (Loredo 2004; Hogg et al. 2010; Mandel 2010; Mandel et al. 2019; Farr 2019).”
Binary Black Hole Population Properties Inferred from the First and Second Observing Runs of Advanced LIGO and Advanced Virgo (2018, methodology): “…used in the O1 mass distribution analysis (Equation (D10) of Abbott et al. 2016c), which fit only for the shape, not the rate/normalization of the mass distribution, if one marginalizes over the rate parameter with a flat-in-log prior p(R0)∝1/R0 (Fishbach et al. 2018; Mandel et al. 2019).”
Constraints on the Cosmic Expansion History from GWTC–3 (2021, background): “Given a set of Nobs GW detections associated with the data {x} = (x1, ..., xNobs), the posterior on Φ can be expressed as (Mandel et al. 2019; Thrane & Talbot 2019; Vitale et al. 2020) p(Φ|{x}, Nobs) = p(Φ) Nobs∏ i=1 ∫ p(xi|Φ, θ)ppop(θ|Φ)dθ∫ pdet(θ,Φ)ppop(θ|Φ)dθ , (1) where p(Φ) is a prior on the…”
One Channel to Rule Them All? Constraining the Origins of Binary Black Holes Using Multiple Formation Pathways (2020, positive): “…j ) π(~θki ) , (2) where Nobs is the number of GW events, Si are the posterior samples used for event i, π(~θk) is the prior weight for each posterior sample in the LVC analysis, and ξ̃χ,α ≡ ∑ j βj ∫ Pdet(~θ)p(~θ|µχ,αj )d~θ is the detection efficiency of each hypermodel (e.g., Mandel et al. 2019).”
An introduction to Bayesian inference in gravitational-wave astronomy: Parameter estimation, model selection, and hierarchical models (2018, background): “We loosely follow the arguments from Abbott et al. (2016a); however, see also Mandel et al. (2018); Fishbach et al. (2018).”
Two populations of LIGO-Virgo black holes (2020, background): “Moreover, we do not include the θ(SNR−SNRc) factor for rejecting events with a low signal-to-noise-ratio as the likelihood is constructed from observed events [66].”