(MAP) adaptation of the MCMC scheme results in considerable gain in computational efficiency.
We demonstrate also that a novel dynamic programming (DP) algorithm for branch length factorization, useful both in the hill-climbing and in the MCMC setting, further reduces computation time.
One might think that a model containing a birth-death prior on the tree branching would necessarily be consistent with a molecular clock, since the birth-death process generates ultrametric trees.
The molecular clock can be avoided, however, by modeling the substitution rates and branching times separately.
We further introduce a dynamic programming (DP) algorithm for optimal factorization of branch lengths into rates and times, thereby considerably reducing the computation time needed for hill-climbing as well as MCMC-algorithms.
The nucleotide substitution is modeled by a continuous-time Markov process and we use a birth-death process to obtain an ].
We perform simulations to show that with our method fast simultaneous inference of substitution rates and branching times for a given tree topology is not only feasible on large trees but also largely unaffected by local-optima problems.