Figure 6

Figure 6 — The inner workings of an MCMC analysis. The two figures on the left show the posterior probabilities of a range of possible trees on the x axis, and the probabilities of these trees on the y axis. The far left shows any single iteration of the algorithm — the current tree might be the star coloured in green, and a change to the tree shape might improve the posterior probability (and move the tree to A). Any such change will be accepted. Another change might move the tree towards a lower posterior probability (B). Such changes would only occasionally be accepted. If you do this repeatedly, as shown in the middle figure, from a starting point marked by the blue star, then eventually the algorithm will sample the areas of highest probability the most, and we can summarize those trees. Because there are actually lots of dimensions here, we can think of the trees as two coordinates. The figure on the right shows this, with the peaks coming out of the page towards us. The exploration by the MCMC chain from the middle panel could be represented equally well as that on the right.