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Divergence time estimation using molecular sequence data relying on uncertain fossil calibrations is an unconventional statistical estimation problem. As the sequence data provide information about the distances only, estimation of absolute times and rates has to rely on information in the prior, so that the model is only semi‐identifiable. In this paper, we use a combination of mathematical analysis, computer simulation, and real data analysis to examine the uncertainty in posterior time estimates when the amount of sequence data increases. The analysis extends the infinite‐sites theory of Yang and Rannala, which predicts the posterior distribution of divergence times and rate when the amount of data approaches infinity. We found that the posterior credibility interval in general decreases and reaches a non‐zero limit when the data size increases. However, for the node with the most precise fossil calibration (as …