Both coalescent constant population size and Yule speciation tree prior yielded similar topology.
For the 4 estimates, the gamma prior returns the posterior mean of 1.05 (95% posterior interval [PI] = 1.02 1.10), whereas the normal prior yields the posterior mean of 1.08 (0.96–1.08).
Likewise, BEAST analyses using Yule as tree prior yielded the highest likelihood harmonic means, but provided no strong evidence as compared to the more complex birth-death models.
In contrast, dating with the birth-death prior yielded Neogene diversifications, and four rate shifts, one for each of the four richest genera.
As shown by [ 19], the incorporation of the informative prior yields the largest increase in performance, but the other components also contribute.
Our sensitivity analysis using an empirical prior yielded some comparisons that did meet the traditional 5% threshold, ie, itraconazole and voriconazole had lower IFI risk and posaconazole and voriconazole had lower IA risk than fluconazole.
This prior yields an analytic form for the posterior model probabilities P r(M k | D), namely 2 log p (M k | D ) / p (M 0 | D ) = (n - 1 ) log (1 + g (1 - R k 2 ) ) - (n - d k - 1 ) log (1 + g ) - 2 ∑ h ∈ M k log π hi 1 - π hi, where M0 is the null model with no regulators, d k is the number of regulators present in model M k, and R k 2 is the R value for M k.
First, an open question is whether there exist general conditions under which reference priors yield proper posterior distributions.
In addition, we have shown through a simulation study that both priors yield procedures that have better frequentist properties than procedures resulting from a competing noninformative prior.
Noninformative priors yield Bayesian inferences that are very similar to frequentist inference.
