GPU-accelerated hierarchical Bayesian estimation of luminosity functions using flux-limited observations with photometric noise

J. M. Szalai-Gindl, T. J. Loredo, B. C. Kelly, I. Csabai, T. Budavári, L. Dobos

Research output: Contribution to journalArticle

Abstract

We describe a C++ framework that uses graphical processing units (GPUs) to accelerate basic hierarchical Bayesian computation, and use it to compute the posterior distribution for the parameters of a galaxy luminosity function based on data with photometric noise and selection effects arising from a flux-limited detection threshold. In addition to estimating the population-level luminosity function parameters, the framework also provides estimates of the absolute magnitude of each object, which automatically correct for Eddington bias. To sample the posterior, we implement a Metropolis–Hastings-within-Gibbs algorithm that alternates between exploring the population-level and member-level parameters. The algorithm exploits conditional independence in hierarchical Bayesian models, which makes member-level exploration readily parallelizable on a GPU. The framework uses adaptive MCMC, automatically tuning Metropolis–Hastings proposal distributions on-the-fly. We present a simulation study demonstrating the accuracy and computational scaling of the algorithm. In addition, we compare hierarchical Bayesian estimation with maximum likelihood estimation (known to provide inconsistent estimates in this setting), providing a concrete demonstration of the benefits of using hierarchical models for luminosity function inference.

Original languageEnglish
Pages (from-to)247-256
Number of pages10
JournalAstronomy and Computing
Volume25
DOIs
Publication statusPublished - Oct 1 2018

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Luminance
luminosity
Fluxes
Processing
Galaxies
Maximum likelihood estimation
Demonstrations
estimates
Tuning
inference
Concretes
proposals
estimating
tuning
galaxies
scaling
simulation
thresholds
parameter
distribution

Keywords

  • Astrostatistics
  • Graphical processing units (GPUs)
  • Hierarchical Bayesian models
  • Markov processes
  • Metropolis-within-Gibbs sampling
  • Parallel computing

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Computer Science Applications
  • Space and Planetary Science

Cite this

GPU-accelerated hierarchical Bayesian estimation of luminosity functions using flux-limited observations with photometric noise. / Szalai-Gindl, J. M.; Loredo, T. J.; Kelly, B. C.; Csabai, I.; Budavári, T.; Dobos, L.

In: Astronomy and Computing, Vol. 25, 01.10.2018, p. 247-256.

Research output: Contribution to journalArticle

Szalai-Gindl, J. M. ; Loredo, T. J. ; Kelly, B. C. ; Csabai, I. ; Budavári, T. ; Dobos, L. / GPU-accelerated hierarchical Bayesian estimation of luminosity functions using flux-limited observations with photometric noise. In: Astronomy and Computing. 2018 ; Vol. 25. pp. 247-256.
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