  We benchmark the reliability of the Rotation Measure (RM) synthesis algorithm
using the 1005 Centaurus A field sources of Feain et al. (2009). The RM
synthesis solutions are compared with estimates of the polarization parameters
using traditional methods. This analysis provides verification of the
reliability of RM synthesis estimates. We show that estimates of the
polarization parameters can be made at lower S/N if the range of RMs is
bounded, but reliable estimates of individual sources with unusual RMs require
unconstrainted solutions and higher S/N.
  We derive from first principles the statistical properties of the
polarization amplitude associated with RM synthesis in the presence of noise.
The amplitude distribution depends explicitly on the amplitude of the
underlying (intrinsic) polarization signal. Hence it is necessary to model the
underlying polarization signal distribution in order to estimate the
reliability and errors in polarization parameter estimates. We introduce a
Bayesian method to derive the distribution of intrinsic amplitudes based on the
distribution of measured amplitudes.
  The theoretically-derived distribution is compared with the empirical data to
provide quantitative estimates of the probability that an RM synthesis solution
is correct as a function of S/N. We provide quantitative estimates of the
probability that any given RM synthesis solution is correct as a function of
measured polarized amplitude and the intrinsic polarization amplitude compared
to the noise.
