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An interesting alternative to avoid the ML multi-dimensional search is to use the mean likelihood estimator combined with the importance sampling technique [9, 10].
This is because, unlike the harmonic mean likelihood, parsimony statistics such as the retention index can only be used in reference to a single topology.
Likelihood maps from studies of the same condition were grouped together and averaged into a mean likelihood map of that condition.
Allowing different rates for each character partition slightly worsened the harmonic mean likelihood compared to the base model (−510.13 versus −509.36, Bayes factor = 1.48 in favor of the base model).
The harmonic mean likelihood from the Metropolis-coupled Markov chain Monte Carlo (MCMCMC) iterations (after burnin was discarded) was used as an approximation to the marginal log-likelihood of the data [16].
A mean likelihood test was performed to generate p values.
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A simple model with a symmetric rate and no cross-site rate variation yielded the best posterior probability as reflected by the harmonic mean likelihoods across the MCMC chains (Table 1).
Under an initial assumption that treats all models as equally probable ('flat priors'), our posterior belief in one model over the other model is reflected by differences in the harmonic mean likelihoods generated by each model [50].
Only H-inco was a protection factor for CHE, which unsurprisingly means likelihood of CHE decreases with increasing household income.
Here, MeanDistance measures the mean belonging likelihood, the less value the MeanDistance has, the more likelihood this component belong to the vertex t.
I don't mean the likelihood of a black American President, though that's mind-bending enough.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com