Lognormal or inv_gamma prior for positive parameter?

Here’s the relevant fragment of source code,

transformed data {
  real alphaShape = 15;
  // ...
parameters {
  real<lower=0> alpha;
  vector<lower=0>[NTHRESH] threshold;
  // ...
model {
  threshold ~ lognormal(-1, 0.5);
  alpha ~ inv_gamma(alphaShape, 1.749*(alphaShape+1));
  // ...

Both lognormal and inv_gamma provide roughly the same shape prior. My model recovers simulated parameters reasonably well; I’m testing with simulation-based calibration. Is there any reason to prefer one or the other type of prior? Maybe easier to read the model if both are one or the other?

Sorry that your question slipped through. Prior choice usually requires domain-specific knowledge and can’t be answered purely on theoretical grounds. A good practical workflow are the prior predictive checks as described in the Visualisation paper. Alternatively, you can fit your model with multiple priors and report how your results change based on prior choice (both the family and the parameters).

Best of luck with your model!

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