Justifying lognormal priors in BEAST

[Daniel Eusebio Quintero Vallejo]

Hi everyone,

I’m currently working on a time-calibrated phylogeny using BEAST and fossil calibrations. For most fossils, I only have a confident estimate of the minimum age of the lineage, but there is little to no information to justify a maximum age. Based on the literature and some advices, I decided to use lognormal priors with the fossil age as the offset, and both the mean and standard deviation set to 1 (in log-space). This approach seems to offer a flexible but not overly restrictive distribution, which reflects the uncertainty in the fossil record.

Does this approach make sense to others in the community? So far, the divergence dates I obtain are consistent with previous studies and with biogeographic expectations, so I’m wondering if this parameterization is acceptable or if there’s any potential issue I might be overlooking. I’d appreciate any feedback or suggestions. Thanks!

[Jordan Douglas]

Hi Daniel,

I think the lognormal is a good choice, as opposed to normal (which allows negative values) or a uniform (which is also quite an unnatural way of dealing with numbers across different orders of magnitude).

But I advise against using the offset. The offset is quite strict and it is assuming there is absolutely zero error on the fossil dating. In practice,  it might turn out that the node is estimated to be younger than the fossil, which would indicate a deeper problem, but using an offset is masking the issue. Instead, I suggest you use a lognormal where the lower 0.5 or 2.5 percentile is at the "minimum" and the upper 99.5 or 97.5 percentile at what you conservatively consider to be the maximum possible age of the clade. Thus, 99% or 95% of the prior probability density is in the sensible zone.

Here is a blog with an R script to help you find the two lognormal parameters that fit to these constraints

https://www.beast2.org/2017/05/05/using-r-to-estimate-probability-distribution-parameters-using-quantiles-or-hpd-intervals.html

Hope this help,

Jordan 

[Daniel Eusebio Quintero Vallejo]

Hi Jordan,

Thank you very much for your detailed response and helpful explanation. I appreciate your insights and the R script reference — it’s a great resource

Just to clarify: in cases where the fossil age is relatively reliable (e.g., well-dated strata with clear taxonomic assignment), do you think using an offset is still defensible as a conservative lower bound? Or would you always recommend using the quantile-based method instead?

Thanks again for your thoughtful advice.

Daniel

[Jordan Douglas]

Hi Daniel,

Personally, I don't think that offsets (or minimums or maximums) are appropriate in general, unless there is a theoretical reason,  like for example rates should be non-negative and proportions should be between 0 and 1, etc. In the example you describe, I would still use a distribution that has non-zero (but very small) probability under the minimum, just in case you are slightly wrong. There is a very large difference between 0 probability and a tiny non-zero probability (that epsilon is what drives people to buy lotto tickets after all). And if it turns out that this minimum is not supported by the data, then you would rather know so you can understand why. But the offset is just hiding the problem. This is just my view, others might disagree.

I wouldn't say the offset is "indefensible" but it is certainly not the best choice.

Jordan