Figure 8. Estimation accuracy as a function of the number of hidden states.

The boxplots show the estimated parameters (divergence time, ancestral effective population size, and recombination rate) for 100 simulated data sets. The true value is showed as the blue dashed line. The number of states in the HMM, i.e. the number of coalescence time intervals used for the estimation takes the values 5, 10 and 15. There is a clear bias in the estimates where we tend to underestimate the divergence time and overestimate the effective population size. This bias is caused by the discretisation of continuous coalescence times into fixed intervals, and the bias is reduced as the number of states (i.e. intervals) increases. The recombination rate is under-estimated, which is a consequence of the Markov assumption.