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Measurement Errors in Astrostatistics

Measurement Errors in Astrostatistics

This video was recorded at NIPS Workshops, Sierra Nevada 2011. Automatic quasar detection is a problem of fundamental importance in modern astronomy. Nonparametric classification techniques based on kernel density estimation (KDE) have been used to develop highly accurate methods of quasar detection, and fast algorithms using space-partitioning trees have made it possible to use these methods on large data sets (Riegel and Gray, 2008). However, astronomical observations come with estimates of measurement errors due to very different inaccuracies, for example, at different distances – and until now, these estimates have been ignored in the KDE approach to quasar detection though they have been demonstrated to improve the accuracy of recent parametric approaches. If the measurement errors are independent and identically distributed, deconvolution of the density estimate with the known error distribution gives an estimate of the error-free distribution. However, when the error magnitude depends on the data point (i.e., in the case of heteroscedastic errors), straightforward deconvolution does not work. We will describe an extension of KDE that makes use of the estimates of heteroscedastic measurement errors, and a fast algorithm for the evaluation of the relevant sums. We present preliminary results on the Sloan Digital Sky Survey data set.


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