To calculate the rate of nucleotide substitution, we require a measurement of the number of nucleotide substitutions occurring in a given time interval. Starting from a given set of aligned sequences {s 1 , ..., s n } for n taxa, we define the pairwise distance in number of substitutions to be the estimates {K ij } under a given model of nucleotide substitution. Naturally the unobservable true values {D ij } of the pairwise distances differ from their estimates {K ij }. To understand this difference, we associate each D ij with an error ε ij and assume that ε ij tends to zero as sequence lengths increase without bound. We further assume that the covariance between errors, cov(ε ij ; ε mn ), is bounded and known. For time measurements, we assume that each sequence is labeled by a sampling time t i given in consistent units. Since we know only the sampling time of a given sample up to the unit of time reported (day, month, year) we posit an uniform error ν i ~ U [0, 1] underlying each t i over the unit sampling interval. To complete the error structure specification we force the two forms of error (ν i and ε ij ) to be independent. Finally, for a set of three sequences (s i , s j , s k ) and their associated pairwise distances, we enforce a fixed topology among sequences, as shown in Figure 1 , via methods outlined in [26] . We augment the topology with the observed sampling times of the three sequences, α, the divergence time between the two sequences of interest and β, the divergence time of all sequences. When necessary for clarity, we write α ij to indicate the true time of divergence between sequences i and j.