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

Sufficient statistics are combinations of data in terms which the likelihood function can be rewritten without loss information. Depending on volume reduction, use sufficient as a preliminary step Bayesian analysis lead to significant increases efficiency when sampling from posterior distributions model parameters. Here we show that frequency integrand cross-correlation statistic and its variance approximate for ground-based searches stochastic gravitational-wave backgrounds. The because one works weak-signal approximation uses measured estimates autocorrelated power each detector. We perform analytic numerical calculations that, this approximation, LIGO-Virgo's hybrid frequentist-Bayesian parameter estimation is equivalent fully analysis. This work closes gap LIGO-Virgo literature suggests directions additional searches.