We describe a process for cross-calibrating the effective areas of X-ray telescopes that observe common targets. The targets are not assumed to be "standard candles" in the classic sense, in that the only constraint placed on the source flux is that it is the same for all instruments. We apply a technique developed by Chen et al. (submitted to J. Amer. Stat. Association) that involves a popular statistical method called shrinkage estimation, which effectively reduces the noise in disparate measurements by combining information across common observations. We can then determine effective area correction factors for each instrument that brings all observatories into the best agreement, consistent with prior knowledge of their effective areas. We have preliminary values that characterize systematic uncertainties in effective areas for almost all operational (and some past) X-ray astronomy instruments in bands covering factors of two in photon energy from 0.15 keV to 300 keV. We demonstrate the method with several data sets from Chandra and XMM-Newton.
A common frustration in signal processing and, more generally, information recovery is the presence of irregularities
in the data. At best, the standard software or methods will no longer be directly applicable when
data are missing, incomplete or irregularly spaced (e.g., as with wavelets). Self-consistency is a very general
and powerful statistical principle for dealing with such problems. Conceptually it is extremely appealing, for it
is essentially a mathematical formalization of iterating
common-sense "trial-and-error" methods until no more
improvement is possible. Mathematically it is elegant, with one
fixed-point equation to solve and a general
projection theorem to establish optimality. Practically it is straightforward to program because it directly uses
the regular/complete-data method for iteration. Its major disadvantage is that it can be computationally intensive.
However, increasingly efficient (approximate) implementations are being discovered, such as for wavelet
de-noising with hard and soft thresholding. This brief overview summarizes the author's keynote presentation on
those points, based on joint work with Thomas Lee on wavelet applications and with Zhan Li on the theoretical
properties of the self-consistent estimators.
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