Title: 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.