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(abridged) We develop an algorithm for estimating parameters of adistribution sampled with contamination, employing a statistical techniqueknown as ``expectation maximization'' (EM). Given models for both member andcontaminant populations, the EM algorithm iteratively evaluates the membershipprobability of each discrete data point, then uses those probabilities toupdate parameter estimates for member and contaminant distributions. The EMapproach has wide applicability to the analysis of astronomical data. Here wetailor an EM algorithm to operate on spectroscopic samples obtained with theMichigan-MIKE Fiber System (MMFS) as part of our Magellan survey of stellarradial velocities in nearby dwarf spheroidal (dSph) galaxies. These samples arepresented in a companion paper and contain discrete measurements ofline-of-sight velocity, projected position, and Mg index for ~1000 - 2500 starsper dSph, including some fraction of contamination by foreground Milky Waystars. The EM algorithm quantifies both dSph and contaminant distributions,returning maximum-likelihood estimates of the means and variances, as well asthe probability that each star is a dSph member. Applied to our MMFS data, theEM algorithm identifies more than 5000 probable dSph members. We test theperformance of the EM algorithm on simulated data sets that represent a rangeof sample size, level of contamination, and amount of overlap between dSph andcontaminant velocity distributions. The simulations establish that for samplesranging from large (N ~3000) to small (N~30), the EM algorithm distinguishesmembers from contaminants and returns accurate parameter estimates much morereliably than conventional methods of contaminant removal (e.g., sigmaclipping).

the astronomical journal

Clean Kinematic Samples in Dwarf Spheroidals: An Algorithm for  Evaluating Membership and Estimating Distribution Parameters When  Contamination is Present