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Since the exponential model was the one with the highest marginal likelihood for both HIV-1A and B Albanian data sets (see supplemental Table S2), we could use the population growth rate, r, which is one of the two free parameters (the other is the number of effective infections Ne) of the model to infer the epidemiological quantity R0.
We estimate the evidence (marginal likelihood) for each model to quantitatively evaluate the alternative models.
The third row provides the log marginal likelihood for each model obtained by thermodynamic integration.
Using their so-called annealing or melting approach one model at a time is evaluated, resulting in a marginal likelihood for each model.
For a detailed discussion on the derivation of the formulas of the marginal likelihood for multinomial and linear Gaussian conditional probability distributions see e.g. [ 42, 43].
From now on, when we refer to the marginal likelihood, we mean the marginal likelihood for a specific model and we forego conditioning on the model Mk in the notation.
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We calculated approximate marginal likelihoods for each coalescent model via importance sampling using the harmonic mean of the sampled likelihoods (with the posterior as the importance distribution) [40].
We calculated approximate marginal likelihoods for each coalescent model via importance sampling (1000 bootstraps) using the harmonic mean of the sampled likelihoods with the posterior as the importance distribution [39].
Thus, comparing marginal likelihoods for model selection between the singlet and triplet models may not provide the whole picture.
We calculated approximate marginal likelihoods for each model via importance sampling using the harmonic mean of the sampled likelihoods (with the posterior as the importance distribution; see [ 27]).
Two ongoing challenges in Bayesian computation relevant to CheMA include inference of model parameters and computation of marginal likelihoods for model selection.
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