Reference prior for proportional odds model

Hi all, let’s say that one is interested in estimating a proportional odds ratio between a single binary exposure and an ordinal outcome with J categories using Bayesian inference: what is a standard form of a reference prior (i.e. a prior that is invariant to re-parametrisation for the proportional log-OR (if there is a known form) and/or is there a way to specify a reference prior for this proportional log-OR in existing software, say in Stan?

Thanks in advance!

Priors on either the intercept or on the slopes are link-dependent, and dependent on final transformations (e.g., risk differences vs. odds ratios), so I’m not sure why you are asking this. And I wasn’t clear whether you were speaking more about intercepts or more about slopes.