Figure 5.—

Illustration of the relationship between various CSDs. The CSD at the head of each arrow can be seen as an approximation to the CSD at the tail. Each arrow is also annotated with a (short) description of this approximation. The CSDs below the dashed line can be cast as an HMM: Those above the dotted line (including a continuous-state version of , which we denote ) have a continuous and infinite state space, while those below have a finite and discrete state space and are therefore amenable to simple dynamic programming algorithms. For more thorough descriptions of each approximation, see the main text and also Paul and Song (2010). Recall in particular that the equality holds only for conditionally sampling a single haplotype.