Version 1.2

A new way of counting MCMC steps

There are several changes that can be made to the model in the MCMC proposal step:
  1. Changes in the branch lengths
  2. Change of the transition-transversion ratio
  3. Changes in the equilibrium frequencies of the nucleotides
  4. Changing the sequence of hidden states
  5. Change of lambda (one minus recombination probability)
Which changes are actually carried out is model-dependent. For example, in the Jukes-Cantor model, the transition-transversion ratio and the equilibrium frequencies are constants rather than free parameters; hence steps 2 and 3 would be left out. In the original version, each individual step was counted as a separate MCMC step. In the new version, all steps together constitute one MCMC step. The motivation for this change is as follows. Assume you have experimented with the Jukes-Cantor model as a starting model and have found that it takes about 10,000 steps, say, to reach the equilibrium distribution. If you now were to switch to the Felsenstein 84 model, you would have to increase the number of MCMC steps by a factor of 5/3 to about 16667 in order to have the equivalent amount of equilibration. This is because now two in five steps are used to update the new parameters, which were not updated in the Jukes-Cantor model. In order to prevent you from having to recompute the equivalent number of MCMC steps every time you switch between models, the new version bundles all the individual update steps together and counts them as one single MCMC step.

A new way of sampling lambda

Lambda, the parameter that determines the difficulty of changing topology, is sampled with Gibbs sampling rather than with the Metropolis-Hastings algorithm. To this end, lambda is first redefined such that it has a conjugate prior in the form of a beta distribution. The updating of the parameters of the posterior distribution and the sampling of lambda is done according to equation (2.3) in C.P. Robert et al., Statistics & Probability Letters 16 (1), 77-83, 1993. Further details and the new options of the program are discussed here.

Simulated annealing

In principle, the initialisation of the hidden states is unimportant since the Markov chain will forget its initial configuration and converge to the equilibrium distribution irrespective of its starting point. In practice, however, extreme starting values could slow down the mixing of the chain and result in a very long burn-in, in which case the MCMC sampler may fail to converge towards the main support of the posterior distribution. In Version 1.2, an annealing scheme has been implemented to improve mixing of the Markov chain and make it easier for the sampling process to leave an extreme initialisation.

Here is a detailed description of the changes .

Last modified: 6 July 2001

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