The marginal likelihood is commonly used for comparing different evolutionary models in Bayesian phylogenetics and is the central quantity used in computing Bayes Factors for comparing model fit. A popular method for estimating marginal likelihoods, the harmonic mean (HM) method, can be easily computed from the output of a Markov chain Monte Carlo analysis but often greatly overestimates the marginal likelihood. The thermodynamic integration (TI) method is much more accurate than the HM method but requires more computation. In this paper, we introduce a new method, steppingstone sampling (SS), which uses importance sampling to estimate each ratio in a series (the "stepping stones") bridging the posterior and prior distributions. We compare the performance of the SS approach to the TI and HM methods in simulation and using real data. We conclude that the greatly increased accuracy of the SS and TI methods argues for their use instead of the HM method, despite the extra computation needed.

Twelve weeks of treatment with ABT-450/r-ombitasvir and dasabuvir without ribavirin was associated with high rates of sustained virologic response among previously untreated patients with HCV genotype 1 infection. Rates of virologic failure were higher without ribavirin than with ribavirin among patients with genotype 1a infection but not among those with genotype 1b infection. (Funded by AbbVie; PEARL-III and PEARL-IV ClinicalTrials.gov numbers, NCT01767116 and NCT01833533.).

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In this phase 2b study, all-oral regimens of antiviral agents and ribavirin were effective both in patients with HCV genotype 1 infection who had not received therapy previously and in those who had not had a response to prior therapy. (Funded by AbbVie; ClinicalTrials.gov number, NCT01464827.).