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Abstract:
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Many astrophysical analyses depend on estimates of galaxy redshift (a proxy for distance) determined from photometric (i.e., imaging) data. Photometric redshift uncertainties can result in large systematic errors in down-stream analysis. Many photometric redshift methods aim to accurately estimate uncertainties; the output can be treated as "photo-z" estimates of the probability density of redshift z given photometric data x, or p(z|x). Open problems are how best to assess the accuracy of these conditional density estimates, and how to use diagnostics to improve estimates of p(z|x). In this talk, I will describe a new statistical framework for assessing conditional density estimates and empirical conditional coverage of prediction sets. The approach provides easy-to-interpret diagnostics of modes of failure, together with practical procedures for recalibrating conditional density estimates and prediction sets to achieve approximate finite-sample coverage. We illustrate our diagnostics and recalibration approach on galaxy photo-z estimation, as well as hurricane intensity estimation based on sequences of satellite image data.
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