Mixture models for studying stellar populations. I - Univariate mixture models, parameter estimation, and the number of discrete population components

A unified approach to the analysis of stellar populations through the application of finite mixture models is presented, and the statistical properties of univariate finite mixture models are examined. A review is presented of the analysis methods that are available, with emphasis on methods for estimating the parameters that describe the underlying stellar populations and for determining the number of discrete stellar populations. Attention is restricted to five variables: U, V, W, Fe/H, and age. Parameter and error estimation is demonstrated in two simulation experiments designed to assess the detectability of a thick disk in samples of solar neighborhood stars.