Extracting distribution parameters from multiple uncertain observations with selection biases

Ilya Mandel, Will Meierjurgen Farr, Jonathan Gair

Research output: Contribution to journalArticleResearchpeer-review

Abstract

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.
Original languageEnglish
JournalMonthly Notices of the Royal Astronomical Society
Publication statusAccepted/In press - 9 Apr 2019

Keywords

  • gravitational waves
  • stars: neutron
  • methods: data analysis

Cite this

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title = "Extracting distribution parameters from multiple uncertain observations with selection biases",
abstract = "We derive a Bayesian framework for incorporating selection effects into populationanalyses. We allow for both measurement uncertainty in individual measurementsand, 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.",
keywords = "gravitational waves, stars: neutron, methods: data analysis",
author = "Ilya Mandel and Farr, {Will Meierjurgen} and Jonathan Gair",
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journal = "Monthly Notices of the Royal Astronomical Society",
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Extracting distribution parameters from multiple uncertain observations with selection biases. / Mandel, Ilya; Farr, Will Meierjurgen; Gair, Jonathan.

In: Monthly Notices of the Royal Astronomical Society, 09.04.2019.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Extracting distribution parameters from multiple uncertain observations with selection biases

AU - Mandel, Ilya

AU - Farr, Will Meierjurgen

AU - Gair, Jonathan

PY - 2019/4/9

Y1 - 2019/4/9

N2 - We derive a Bayesian framework for incorporating selection effects into populationanalyses. We allow for both measurement uncertainty in individual measurementsand, 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.

AB - We derive a Bayesian framework for incorporating selection effects into populationanalyses. We allow for both measurement uncertainty in individual measurementsand, 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.

KW - gravitational waves

KW - stars: neutron

KW - methods: data analysis

M3 - Article

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

ER -