Comparing cosmic microwave background datasets

Abstract

To extract reliable cosmic parameters from cosmic microwave background datasets, it is essential to show that the data are not contaminated by residual non-cosmological signals. We describe general statistical approaches to this problem, with an emphasis on the case in which there are two datasets that can be checked for consistency. A first visual step is the Wiener filter mapping from one set of data onto the pixel basis of another. For more quantitative analyses, we develop and apply both Bayesian and frequentist techniques. We define the “contamination parameter” and advocate the calculation of its probability distribution as a means of examining the consistency of two datasets. The closely related “probability enhancement factor” is shown to be a useful statistic for comparison; it is significantly better than a number of ${\chi }^2$ quantities we consider. Our methods can be used internally (between different subsets of a dataset) or externally (between different experiments), for observing regions that completely overlap, partially overlap or overlap not at all, and for observing strategies that differ greatly. We apply the methods to check the consistency (internal and external) of the MSAM92, MSAM94 and Saskatoon Ring datasets. From comparing the two MSAM datasets, we find that (given a particular model of the contaminant) the most probable level of contamination is 12%, with no contamination only 1.05 times less probable, 50% contamination about 8 times less probable and 100% contamination strongly ruled out at over $2\times {10}^5$ times less probable. From comparing the 1992 MSAM flight with the Saskatoon data, we find the most probable level of contamination to be 50%, with no contamination only 1.6 times less probable and 100% contamination 13 times less probable. Our methods can also be used to calibrate one experiment off of another. To achieve the best agreement between the Saskatoon and MSAM92 data, we find that the MSAM92 data should be multiplied by (or Saskatoon data divided by) ${1.06}_{-0.26}^{+0.22\mathrm{}}.$