Sentence examples for marginal likelihoods to from inspiring English sources

However, given the sensitivity of marginal likelihoods to the prior, care is needed when selecting prior distributions [ 14].

We set K between 1-15, and performed 10 replicates for each value of K. Pritchard et al. [ 68] suggest a method based upon marginal likelihoods to determine the minimal number of populations needed to explain the data.

We compare the accuracy of the RLC and UCLN clock models in retrieving the known crown age of the long-stemmed clade, and also use marginal likelihoods to determine which model is the better fit.

As the crown age of Xanthorrhoea is unknown, we compare the performance of the UCLN and RLC clock models using marginal likelihoods to determine which is the better fit.

We used stepping-stone sampling [ 44] to obtain estimates of the marginal likelihoods to choose between different clock models: the strict clock, a relaxed, auto-correlated log-normal clock (TK02 [ 45]), and a relaxed, uncorrelated gamma clock model (the white-noise or independent gamma rates (IGR) model [ 46]).

Finally, the third stage applies the reference prior approach to the marginal likelihood to obtain the reference prior for the parameter of interest.

This is a computationally intensive approach which yields reliable estimates for the (log) ratio of the marginal likelihoods corresponding to two models.

Given that models with many divergence events can have small marginal likelihoods due to the uniform priors on divergence-time parameters, the U-shaped prior will effectively create a strong prior preference for models with very few divergence events.

Although the harmonic mean is not the best estimator of the marginal likelihoods used to compute the Bayes Factor, alternative methods [ 75- 77] are either computationally intensive or not readily implementable at this time.

This causes divergence models with more divergence-time parameters to integrate over a much greater parameter space with low likelihood yet high prior density, which can result in small marginal likelihoods relative to models with fewer divergence-time parameters [ 13, 14].

Models that allow for seasonal migration rates between SC and NC and the global community (Table  2) and include seasonality based on the destination community (Additional file 2: Methods 2.7) have the highest marginal likelihood (−561.0 to −561.8) compared to non-seasonal models (marginal likelihood = −587.0, −588.4 without and with variable selection, respectively).