Why Cauchy as prior for residual error in ODE models?


#1

I always have wondered why is so common to give a Cauchy prior to the residual error (\sigma) in ODE models.

From the prior choice recommendations page, I know that a Cauchy distribution can be considered as a weak prior. However, why not give another weakly informative prior to \sigma? Is there a special consideration for this case?.

Thanks in advance!


#2

We’ve been backing away from recommending Cauchy priors, though our manual hasn’t caught up (Andrew’s rewriting it now!). In general, we’re marching toward more and more informative priors, which can lead to improvements in both computation and inference. Mostly, though, we use weakly informative priors on the scale. Say something like normal(0, 1) for values we expect to be roughly 1 in absolute value.

The nice thing about a Cauchy is that you can put most of the probability mass on small values, while still allowing for the odd large value. So if you don’t know the scale of your data, it can be more robust.


#3

See Section 3.1.2 of https://betanalpha.github.io/assets/case_studies/weakly_informative_shapes.html for more discussion.


Cross-classified Hierarchical Model, Heterogenous Variances
#4

Thank you very much for the link. Reading your article was really helpful. I will cite your page, even thought some people in academia considers that information not published in journals is not worth of attention, but it was priceless and much clearer than the few papers that I have found trying to make sense of prior choosing.


#5

Maybe there are people who refuse to read books, blogs, or arXiv papers and refuse to attend lectures or go to workshops due to lack of peer review. I don’t know any.

But I know a lot of people who assert that they only trust peer-reviwed content. This has always struck me as ridiculous given the process of peer review, as I know almost all of these people have spent time on the editorial side, so they’re well acquainted with how the sausage is made.

I do know lots of people who try not to cite anyting that’s not peer reviewed (and doesn’t have a PubMed link and DOI).