Does uneven pairsplot density indicate reparameterization?

Modeling
2

Hi, sorry we took so long to get to your inquiry.

  1. Indeed the pairs plot looks fishy and might be a cause for pathological geometry. Indeed “uneven” density can be problematic - see Mike’s case study for a more in-depth description, if you haven’t already (https://betanalpha.github.io/assets/case_studies/identifiability.html)

  2. I’ve found a slightly obscure reference that has a formula for scaling the Weibull (http://www.math.wm.edu/~leemis/chart/UDR/PDFs/WeibullS.pdf). If I understand it correctly their parametrization is a bit different - they use \alpha, \beta and I think (please check my calculations) that it relates to Stan’s parameterization (I’ll note it as \alpha_{stan}, \sigma) so that:

\alpha = \sigma^{\alpha_{stan}} \\ \beta = \alpha_{stan}

They then show that if Y \sim \mathrm{Weibull}(\alpha, \beta) and Y = kX we have Y \sim \mathrm{Weibull}(\alpha k ^ \beta, \beta)

Transforming for the Stan parametrization we get Y \sim \mathrm{Weibull_{stan}}(\alpha_{stan}, k\sigma). So I think you should be safe scaling your Weibull (but please, check my calculations) and I would expect it to help - at least with this part of the model.

Best of luck with your model!
(also, I enjoyed your StanCon presentation, cool work)

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