Computational AstroStatistics: Fast algorithms and efficient statistics for density estimation in large astronomical datasets

We present initial results on the use of Mixture Models for density estimation in large astronomical databases. We provide herein both the theoretical and experimental background for using a mixture model of Gaussians based on the Expectation Maximization (EM) Algorithm. Applying these analyses to simulated data sets we show that the EM algorithm - using the both the AIC & BIC penalized likelihood to score the fit - can out-perform the best kernel density estimate of the distribution while requiring no "fine-tuning" of the input algorithm parameters. We find that EM can accurately recover the underlying density distribution from point processes thus providing an efficient adaptive smoothing method for astronomical source catalogs. To demonstrate the general application of this statistic to astrophysical problems we consider two cases of density estimation; the clustering of galaxies in redshift space and the clustering of stars in color space. From these data we show that EM provides an adaptive smoothing of the distribution of galaxies in redshift space (describing accurately both the small and large-scale features within the data) and a means of identifying outliers in multi-dimensional color-color space (e.g., for the identification of high redshift QSOs). Automated tools such as those based on the EM algorithm will be needed in the analysis of the next generation of astronomical catalogs (2MASS, FIRST, PLANCK, SDSS) and ultimately in in the development of the National Virtual Observatory.