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Sufficient statistics are combinations of data in terms of which thelikelihood function can be rewritten without loss of information. Depending onthe data volume reduction, the use of sufficient statistics as a preliminarystep in a Bayesian analysis can lead to significant increases in efficiencywhen sampling from posterior distributions of model parameters. Here we showthat the frequency integrand of the cross-correlation statistic and itsvariance are approximate sufficient statistics for ground-based searches forstochastic gravitational-wave backgrounds. The sufficient statistics areapproximate because one works in the weak-signal approximation and usesmeasured estimates of the auto-correlated power in each detector. Usinganalytic and numerical calculations, we prove that LIGO-Virgo's hybridfrequentist-Bayesian parameter estimation analysis is equivalent to a fullyBayesian analysis. This work closes a gap in the LIGO-Virgo literature, andsuggests directions for additional searches.

Frequentist versus Bayesian analyses: Cross-correlation as an (approximate) sufficient statistic for LIGO-Virgo stochastic background searches