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For the proposal step, we have to balance the desire to move
globally through the parameter space with the need to
make computationally feasible moves in areas of high probability.
Therefore we split up the process and we apply a suitable
proposition to the variables at each iteration.
For the frequency parameters we adopt a Dirichlet proposal
distribution centred at the current frequency vector used by
Larget and Simon (1999). For the gamma distribution
parameter and the substitution rate ratios, a normal proposal
distribution centred at the current value is used, with reflecting
boundary at zero and at the upper-limit defined above.
Distant moves in might result in a low acceptance rate
whereas small modifications will prevent a full inspection of
highly probable areas. The parameters used to move into the state
space must therefore be carefully chosen for proper mixing (quick
convergence and good sampling from the posterior probability density).
With *mcmcphase*, these parameters can be adjusted during the burnin
period.

Gowri-Shankar Vivek
2003-04-24