COMPARING COSMIC MICROWAVE BACKGROUND DATASETS - ART. NO. 083004

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 ther e 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 appl y both Bayesian and frequentist techniques. We define the ''contaminat ion parameter'' and advocate the calculation of its probability distri bution as a means of examining the consistency of two datasets. The cl osely related ''probability enhancement factor'' is shown to be a usef ul 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 differe nt experiments), for observing regions that completely overlap, partia lly overlap or overlap not at all, and for observing strategies that d iffer 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 mod el of the contaminant) the most probable level of contamination is 12% , with no contamination only 1.05 times less probable, 50% contaminati on about 8 times less probable and 100% contamination strongly ruled o ut at over 2 x 10(5) times less probable. From comparing the 1992 MSAM flight with the Saskatoon data, we find the most probable level of co ntamination to be 50%, with no contamination only 1.6 times less proba ble and 100% contamination 13 times less probable. Our methods can als o be used to calibrate one experiment off of another. To achieve the b est agreement between the Saskatoon and MAM92 data, we find that the M SAM92 data should be multiplied by (or Saskatoon data divided by) 1.06 (-0.26)(+0.22). [S0556-2821(98)05320-X].