Advantages of Bayesian likelihood

A major advantage of the Bayesian method is the ease with which posterior probabilities can be interpreted (Huelsenbeck et al. 2002). Under the assumption that the evolutionary model is true and that the MCMC has accurately sampled the posterior probability distribution, the posterior probability value represents the probability that the tree is correct given the data and the priors. Similarly, the proportion of trees in the MCMC sample in which a monophyletic group appears represents the probability that the clade is "true," given the caveats of priors, model, and data.

As in maximum likelihood analyses, the result of the Bayesian analysis is dependent on the model of sequence evolution being "correct." Bayesian approaches to phylogeny require a likelihood value of a given tree topology for their calculation of the posterior probability of that evolutionary scenario. The likelihood parameter in the Bayesian method uses the same models and their associated assumptions as the maximum likelihood methods described above, and the caveats inherent in maximum likelihood phylogeny estimation with respect to evolutionary models also apply to Bayesian analysis (see above discussion of likelihood criticisms).

Computational and time constraints require that the posterior probability distribution be approximated using MCMC techniques (Huelsenbeck et al. 2001, 2002). Chains may fail to provide an accurate estimate of posterior probability distributions if they are not allowed to run long enough, or if mixing is a problem due to widely separated peaks in the distribution. It is difficult to know when a chain has run long enough to provide an acceptable estimate of posterior probabilities. The longer the chain is run, the more precise the estimate of posterior probability distribution. Huelsenbeck et al. (2002) propose three recommendations to ensure that the posterior probability is sampled reliably: (1) run several long chains, and check for consistency in results; (2) run multiple chains, each starting from a random tree and check for consistency; and (3) monitor the model parameters for convergence. The Metropolis-coupling technique promotes good mixing and increases the speed of convergence (Huelsenbeck et al. 2001, 2002).

Some view it as an advantage that Bayesian analysis requires the incorporation of previous knowledge or beliefs in terms of prior probabilities. The mechanics of formulating priors can be difficult if one chooses to base these off the results of previous analyses or taxonomy ("complex priors,'' Huelsenbeck et al. 2002). Making the prior probabilities of each tree equal eliminates the use of complex priors, as well as any a priori assumptions that any hypothesis is more probable than any other in light of prior beliefs, clearly this approach is not in the true Bayesian spirit.

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