We develop an algorithm for estimating parameters of a distribution sampled with contamination .
We employ a statistical technique known as “ expectation maximization ” ( EM ) .
Given models for both member and contaminant populations , the EM algorithm iteratively evaluates the membership probability of each discrete data point , then uses those probabilities to update parameter estimates for member and contaminant distributions .
The EM approach has wide applicability to the analysis of astronomical data .
Here we tailor an EM algorithm to operate on spectroscopic samples obtained with the Michigan-MIKE Fiber System ( MMFS ) as part of our Magellan survey of stellar radial velocities in nearby dwarf spheroidal ( dSph ) galaxies .
These samples , to be presented in a companion paper , contain discrete measurements of line-of-sight velocity , projected position , and pseudo-equivalent width of the Mg-triplet feature , for \sim 1000 - 2500 stars per dSph , including some fraction of contamination by foreground Milky Way stars .
The EM algorithm uses all of the available data to quantify dSph and contaminant distributions .
For distributions ( e.g. , velocity and Mg-index of dSph stars ) assumed to be Gaussian , the EM algorithm returns maximum-likelihood estimates of the mean and variance , as well as the probability that each star is a dSph member .
These probabilities can serve as weights in subsequent analyses .
Applied to our MMFS data , the EM algorithm identifies more than 5000 stars as probable dSph members .
We test the performance of the EM algorithm on simulated data sets that represent a range of sample size , level of contamination , and amount of overlap between dSph and contaminant velocity distributions .
The simulations establish that for samples ranging from large ( N \sim 3000 , characteristic of the MMFS samples ) to small ( N \sim 30 , resembling new samples for extremely faint dSphs ) , the EM algorithm distinguishes members from contaminants and returns accurate parameter estimates much more reliably than conventional methods of contaminant removal ( e.g. , sigma clipping ) .