I am using the Metropolis-Hastings algorithm for phylogenetic inference. To do so I would like to draw the substitution matrix Q from the generalized time-reversible model.
To do so I need proposal distributions for the stationary distribution and the 6 substitution probabilities. For the stationary distributions I would use a Dirichlet, but I am not sure what to take for the substitution probabilities.
My question: Can I use a Dirichlet distribution for the substitution probabilities too?
My problem is: Dirichlet samples sum up to 1 but this is not necessarily true for the 6 parameters. The domain of the proposal distribution is only a subset of the domain of the target distribution but every single substitution probability can take all values in [0,1] (Which is everything that matters to me).
I hope you understand my question :D