Mixture Models in Astronomy

Abstract

Mixture models combine multiple components into a single probability density function. They are a natural statistical model for many situations in astronomy, such as surveys containing multiple types of objects, cluster analysis in various data spaces, and complicated distribution functions. This chapter in the CRC Handbook of Mixture Analysis is concerned with astronomical applications of mixture models for cluster analysis, classification, and semi-parametric density estimation. We present several classification examples from the literature, including identification of a new class, analysis of contaminants, and overlapping populations. In most cases, mixtures of normal (Gaussian) distributions are used, but it is sometimes necessary to use different distribution functions derived from astrophysical experience. We also address the use of mixture models for the analysis of spatial distributions of objects, like galaxies in redshift surveys or young stars in star-forming regions. In the case of galaxy clustering, mixture models may not be the optimal choice for understanding the homogeneous and isotropic structure of voids and filaments. However, we show that mixture models, using astrophysical models for star clusters, may provide a natural solution to the problem of subdividing a young stellar population into subclusters. Finally, we explore how mixture models can be used for mathematically advanced modeling of data with heteroscedastic uncertainties or missing values, providing two example algorithms, the measurement error regression model of Kelly (2007) and the Extreme Deconvolution model of Bovy et al. (2011). The challenges presented by astronomical science, aided by the public availability of catalogs from major surveys and missions, are a rich area for collaboration between statisticians and astronomers.

This is a revised preprint of a chapter in the Handbook of Mixture Analysis, edited by S. Früwirth-Schnatter, G. Celeux, and C. P. Robert, published in the "Handbooks of Modern Statistical Methods" series by Chapman & Hall/CRC, 2018; revisions include several additional references and several changes to mathematical notation

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Cited by in corpus (7)

• Modelling unresolved binaries of open clusters in color-magnitude diagram. I. method and application of NGC3532
• Likelihood Non-Gaussianity in Large-Scale Structure Analyses
• Identification of Sagittarius stream members in Angular Momentum space with Gaussian mixture techniques
• Augmenting machine learning photometric redshifts with Gaussian mixture models
• Gaia Parallax of Milky Way Globular Clusters -- A Solution of Mixture Model
• Astro2020 Science White Paper: The Next Decade of Astroinformatics and Astrostatistics
• Classification of Pulsars using Extreme Deconvolution