Beast bayesian dating
As all the sequences were sampled from the same time the data should provide no information about the rate of evolution so we might expect the posterior distribution of rate to simply recover the prior we are using.
This is not significantly different from our prior distribution and thus is behaving nicely the way we expect it to.
So why is the uniform prior on yule.birth Rate working the way we expect when the uniform prior on Size was not?
The answer lies in the way in which the different models are parameterized.
As the parameter is also part of the MCMC state it must also have a prior distribution specified for it.
The default prior distribution is uniform with a very high upper bound.
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If the coalescent prior had been parameterized with a parameter that was equal to 1/Size, then a uniform prior would have behaved nicely (in effect the Jeffreys prior is performing this re-parameterization).