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Bayesian statistical inference has become increasingly important for theanalysis of observations from the Advanced LIGO and Advanced Virgogravitational-wave detectors. To this end, iterative simulation techniques, inparticular nested sampling and parallel tempering, have been implemented in thesoftware library LALInference to sample from the posterior distribution ofwaveform parameters of compact binary coalescence events. Nested sampling wasmainly developed to calculate the marginal likelihood of a model but canproduce posterior samples as a by-product. Thermodynamic integration isemployed to calculate the evidence using samples generated by paralleltempering but has been found to be computationally demanding. Here we proposethe stepping-stone sampling algorithm, originally proposed by Xie et al. (2011)in phylogenetics and a special case of path sampling, as an alternative tothermodynamic integration. The stepping-stone sampling algorithm is also basedon samples from the power posteriors of parallel tempering but has superiorperformance as fewer temperature steps and thus computational resources areneeded to achieve the same accuracy. We demonstrate its performance andcomputational costs in comparison to thermodynamic integration and nestedsampling in a simulation study and a case study of computing the marginallikelihood of a binary black hole signal model applied to simulated data fromthe Advanced LIGO and Advanced Virgo gravitational wave detectors. To deal withthe inadequate methods currently employed to estimate the standard errors ofevidence estimates based on power posterior techniques, we propose a novelblock bootstrap approach and show its potential in our simulation study andLIGO application.

The stepping-stone sampling algorithm for calculating the evidence of gravitational wave models