We introduce a method for analyzing radio interferometry data which produces
maps which are optimal in the Bayesian sense of maximum posterior probability
density, given certain prior assumptions. It is similar to maximum entropy
techniques, but with an exact accounting of the multiplicity instead of the
usual approximation involving Stirling's formula. It also incorporates an Occam
factor, automatically limiting the effective amount of detail in the map to
that justified by the data. We use Gibbs sampling to determine, to any desired
degree of accuracy, the multi-dimensional posterior density distribution. From
this we can construct a mean posterior map and other measures of the posterior
density, including confidence limits on any well-defined function of the
posterior map.Comment: 41 pages, 11 figures. High resolution figures 8 and 9 available at
http://www.astro.uiuc.edu/~bwandelt/SuttonWandelt200