My apologies. You are right to be confused, I had misinterpreted the original post and the code above is not appropriate. von_mises_unitvector_lpdf should actually be used as a prior on mean angle outside of the if(!prior_only){ statement.
//e.g. prior that mu = 0°
target += von_mises_unitvector_lpdf(mu_vec| 0, 1);
von_mises_lpdf was actually still used in the original post, but with an estimate of mu that comes from:
real temp_Intercept = atan2(mu_vec[2], mu_vec[1]);
in the transformed parameters block.
The mu_vec replacement of temp_Intercept remains the one thing that I can’t get into a brms custom_family. Reading the rest of the original thread it seems there may be good reasons not to allow distributional parameters to be overwritten/replaced by transformed parameters, but I’m afraid this discussion goes over my head.
To keep this a brms question, I suppose my question should now be:
“Is it permissible (or wise) to make a brms custom_family in which parameters are estimated via a conversion in the transformed parameters block?”
, before asking whether it can be done.
I’m not sure I understand this well enough to write it in mathematical notation, but I can try to describe what I think is going on. If I’ve now understood correctly, the idea is to have two distributional parameters: a unit_vector[2], which replaces temp_Intercept, and an intercept for kappa (as in brms default von Mises). The unit_vector is then transformed to the temp_Intercept for mean angle in the transformed parameters block (as above), which is then used in the model block. The advantages of this transform are:
- Estimates of mean angle near one another on the circle (e.g.
-3&3) have unit vector equivalents that are close in value on a linear scale (i.e.(-0.14, -0.99)&(0.14, -0.99)), producing good convergence. - Estimation of mean angle as a unit_vector avoids mean angle estimates that exit the -π–π interval
At least from I practical point of view I can confirm that doing this gives the right answers in simulation (much better than in my earlier post, provided something sensible is then done with the random effects on mean angle).
I’ll attach my current stan code for reference. handwritten.uvMEmises6.stan (6.4 KB)