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Extreme deconvolution: inferring complete distribution functions from noisy, heterogeneous and incomplete observations | | Jo Bovy
; David W. Hogg
; Sam T. Roweis
; | | Date: |
19 May 2009 | | Abstract: | We generalize the well-known mixtures of Gaussians approach to density
estimation and the accompanying Expectation-Maximization technique for finding
the maximum likelihood parameters of the mixture to the case where each data
point carries an individual d-dimensional uncertainty covariance and has unique
missing data properties. This algorithm reconstructs the error-deconvolved or
"underlying" distribution function common to all samples, even when the
individual data points are samples from different distributions, obtained by
convolving the underlying distribution with the unique uncertainty distribution
of the data point and projecting out the missing data directions. We show how
this basic algorithm can be extended with Bayesian priors on all of the model
parameters and a "split-and-merge" procedure designed to avoid local maxima of
the likelihood. We apply this technique to a few typical astrophysical
applications. | | Source: | arXiv, 0905.2979 | | Services: | Forum | Review | PDF | Favorites | |
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