Thanks for the discussion @jessegrabowski . The short answer is that I am not trying to estimate the parameters of the log-normal distribution, and the ais Uniform prior is a placeholder for a more complex model.
I have a larger model that simulates sea level rise based on historical datasets, for which the Bayesian likelihood definition is straightforward (my model is the smooth trend, what is the chance of measuring an observation given “noise” occuring in nature, and measurement errors). Now for the projections into the future, I also want to include other constraints that come from independent estimate with physically-based models. They are not direct observations. And these estimates tend to produce a log-normal looking distribution for the Antarctic Ice Sheet (low- but non-zero probability of a high contribution to sea-level from Antarctica), which I sum-up with a known log-normal distribution. I’m not sure what is the best way of integrating that knowledge in the model. If I had only one number (the ais term in the simple model above), I’d use it as a prior distribution. However, the Antarctic contribution comes from an equation involving a few other parameters and exogenous variables (surface air temperature timeseries). So using Potentials is the best (and only) way I found so far. Please let me know if you have a better suggestion.
EDIT: the example above shows that if I have no other information (a uniform prior, no other constraints), then the posterior converges toward the specified log-normal. Now presumably it will also compose nicely along with additional constraints.