A Bayesian approach to calibrating period-luminosity relations of RR Lyrae stars in the mid-infrared

Christopher R. Klein, Joseph W. Richards, Nathaniel Butler, Joshua S. Bloom

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

A Bayesian approach to calibrating period-luminosity (PL) relations has substantial benefits over generic least-squares fits. In particular, the Bayesian approach takes into account the full prior distribution of the model parameters, such as the a priori distances, and refits these parameters as part of the process of settling on the most highly-constrained final fit. Additionally, the Bayesian approach can naturally ingest data from multiple wavebands and simultaneously fit the parameters of PL relations for each waveband in a procedure that constrains the parameter posterior distributions so as to minimize the scatter of the final fits appropriately in all wavebands. Here we describe the generalized approach to Bayesian model fitting and then specialize to a detailed description of applying Bayesian linear model fitting to the mid-infrared PL relations of RR Lyrae variable stars. For this example application we quantify the improvement afforded by using a Bayesian model fit. We also compare distances previously predicted in our example application to recently published parallax distances measured with the Hubble Space Telescope and find their agreement to be a vindication of our methodology. Our intent with this article is to spread awareness of the benefits and applicability of this Bayesian approach and encourage future PL relation investigations to consider employing this powerful analysis method.

Original languageEnglish (US)
Pages (from-to)83-87
Number of pages5
JournalAstrophysics and Space Science
Volume341
Issue number1
DOIs
StatePublished - 2012

Fingerprint

calibrating
luminosity
stars
variable stars
parallax
settling
Hubble Space Telescope
methodology
parameter
distribution

Keywords

  • Distance scale
  • RR Lyrae
  • Statistical methods

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

A Bayesian approach to calibrating period-luminosity relations of RR Lyrae stars in the mid-infrared. / Klein, Christopher R.; Richards, Joseph W.; Butler, Nathaniel; Bloom, Joshua S.

In: Astrophysics and Space Science, Vol. 341, No. 1, 2012, p. 83-87.

Research output: Contribution to journalArticle

Klein, Christopher R. ; Richards, Joseph W. ; Butler, Nathaniel ; Bloom, Joshua S. / A Bayesian approach to calibrating period-luminosity relations of RR Lyrae stars in the mid-infrared. In: Astrophysics and Space Science. 2012 ; Vol. 341, No. 1. pp. 83-87.
@article{86ef70bf4a1f47be93ee5afb4ce0191e,
title = "A Bayesian approach to calibrating period-luminosity relations of RR Lyrae stars in the mid-infrared",
abstract = "A Bayesian approach to calibrating period-luminosity (PL) relations has substantial benefits over generic least-squares fits. In particular, the Bayesian approach takes into account the full prior distribution of the model parameters, such as the a priori distances, and refits these parameters as part of the process of settling on the most highly-constrained final fit. Additionally, the Bayesian approach can naturally ingest data from multiple wavebands and simultaneously fit the parameters of PL relations for each waveband in a procedure that constrains the parameter posterior distributions so as to minimize the scatter of the final fits appropriately in all wavebands. Here we describe the generalized approach to Bayesian model fitting and then specialize to a detailed description of applying Bayesian linear model fitting to the mid-infrared PL relations of RR Lyrae variable stars. For this example application we quantify the improvement afforded by using a Bayesian model fit. We also compare distances previously predicted in our example application to recently published parallax distances measured with the Hubble Space Telescope and find their agreement to be a vindication of our methodology. Our intent with this article is to spread awareness of the benefits and applicability of this Bayesian approach and encourage future PL relation investigations to consider employing this powerful analysis method.",
keywords = "Distance scale, RR Lyrae, Statistical methods",
author = "Klein, {Christopher R.} and Richards, {Joseph W.} and Nathaniel Butler and Bloom, {Joshua S.}",
year = "2012",
doi = "10.1007/s10509-012-1035-4",
language = "English (US)",
volume = "341",
pages = "83--87",
journal = "Astrophysics and Space Science",
issn = "0004-640X",
publisher = "Springer Netherlands",
number = "1",

}

TY - JOUR

T1 - A Bayesian approach to calibrating period-luminosity relations of RR Lyrae stars in the mid-infrared

AU - Klein, Christopher R.

AU - Richards, Joseph W.

AU - Butler, Nathaniel

AU - Bloom, Joshua S.

PY - 2012

Y1 - 2012

N2 - A Bayesian approach to calibrating period-luminosity (PL) relations has substantial benefits over generic least-squares fits. In particular, the Bayesian approach takes into account the full prior distribution of the model parameters, such as the a priori distances, and refits these parameters as part of the process of settling on the most highly-constrained final fit. Additionally, the Bayesian approach can naturally ingest data from multiple wavebands and simultaneously fit the parameters of PL relations for each waveband in a procedure that constrains the parameter posterior distributions so as to minimize the scatter of the final fits appropriately in all wavebands. Here we describe the generalized approach to Bayesian model fitting and then specialize to a detailed description of applying Bayesian linear model fitting to the mid-infrared PL relations of RR Lyrae variable stars. For this example application we quantify the improvement afforded by using a Bayesian model fit. We also compare distances previously predicted in our example application to recently published parallax distances measured with the Hubble Space Telescope and find their agreement to be a vindication of our methodology. Our intent with this article is to spread awareness of the benefits and applicability of this Bayesian approach and encourage future PL relation investigations to consider employing this powerful analysis method.

AB - A Bayesian approach to calibrating period-luminosity (PL) relations has substantial benefits over generic least-squares fits. In particular, the Bayesian approach takes into account the full prior distribution of the model parameters, such as the a priori distances, and refits these parameters as part of the process of settling on the most highly-constrained final fit. Additionally, the Bayesian approach can naturally ingest data from multiple wavebands and simultaneously fit the parameters of PL relations for each waveband in a procedure that constrains the parameter posterior distributions so as to minimize the scatter of the final fits appropriately in all wavebands. Here we describe the generalized approach to Bayesian model fitting and then specialize to a detailed description of applying Bayesian linear model fitting to the mid-infrared PL relations of RR Lyrae variable stars. For this example application we quantify the improvement afforded by using a Bayesian model fit. We also compare distances previously predicted in our example application to recently published parallax distances measured with the Hubble Space Telescope and find their agreement to be a vindication of our methodology. Our intent with this article is to spread awareness of the benefits and applicability of this Bayesian approach and encourage future PL relation investigations to consider employing this powerful analysis method.

KW - Distance scale

KW - RR Lyrae

KW - Statistical methods

UR - http://www.scopus.com/inward/record.url?scp=84866281865&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84866281865&partnerID=8YFLogxK

U2 - 10.1007/s10509-012-1035-4

DO - 10.1007/s10509-012-1035-4

M3 - Article

AN - SCOPUS:84866281865

VL - 341

SP - 83

EP - 87

JO - Astrophysics and Space Science

JF - Astrophysics and Space Science

SN - 0004-640X

IS - 1

ER -