The Redelings-Suchard kernel is a Metropolis-Hastings scheme for sampling a 3-branch alignment (e.g. of three observed sister taxa and their unobserved parent) with the same big-O complexity as sampling a single-branch (pairwise) alignment. The kernel is described in this paper:
- Redelings & Suchard: Joint Bayesian estimation of alignment and phylogeny. Syst. Biol. 2005;54:401-18.