Figure 5.

Slice sampling. An example of slice sampling updating the value of the focal node from Figure 4(A) from θ _i to ${\theta }_i^{\prime }$. First, the conditional probability that the value of the evolving character at the focal node is equal to θ _i – given the other ancestral states and stable model parameters – is calculated. A random number y is drawn from the uniform distribution between zero and this conditional probability (marked with a dotted line). The set of possible values of ${\theta }_i^{\prime }$ is estimated by bracketing regions around the modes of the distribution for which the conditional probability is greater than y (solid lines and shaded region of the distribution). The new value ${\theta }_i^{\prime }$ is drawn as a uniform random variable from this set.