  Bayesian statistical inference has become increasingly important for the
analysis of observations from the Advanced LIGO and Advanced Virgo
gravitational-wave detectors. To this end, iterative simulation techniques, in
particular nested sampling and parallel tempering, have been implemented in the
software library LALInference to sample from the posterior distribution of
waveform parameters of compact binary coalescence events. Nested sampling was
mainly developed to calculate the marginal likelihood of a model but can
produce posterior samples as a by-product. Thermodynamic integration is
employed to calculate the evidence using samples generated by parallel
tempering but has been found to be computationally demanding. Here we propose
the stepping-stone sampling algorithm, originally proposed by Xie et al. (2011)
in phylogenetics and a special case of path sampling, as an alternative to
thermodynamic integration. The stepping-stone sampling algorithm is also based
on samples from the power posteriors of parallel tempering but has superior
performance as fewer temperature steps and thus computational resources are
needed to achieve the same accuracy. We demonstrate its performance and
computational costs in comparison to thermodynamic integration and nested
sampling in a simulation study and a case study of computing the marginal
likelihood of a binary black hole signal model applied to simulated data from
the Advanced LIGO and Advanced Virgo gravitational wave detectors. To deal with
the inadequate methods currently employed to estimate the standard errors of
evidence estimates based on power posterior techniques, we propose a novel
block bootstrap approach and show its potential in our simulation study and
LIGO application.
