Did you actually read and understand the linked example? The entire point of it is that unless you basically craft your prior to mirror the frequentist behavior, your posterior will center on the truth super slowly. And the setting is not very artificial, exposure/outcome relationships w/ baseline covariates often are complicated, and we often do know randomization probabilities in trials.
Why would I want to approximate your posterior if it has this shitty behavior?
Did you actually read and understand the linked example? The entire point of it is that unless you basically craft your prior to mirror the frequentist behavior, your posterior will center on the truth super slowly. And the setting is not very artificial, exposure/outcome relationships w/ baseline covariates often are complicated, and we often do know randomization probabilities in trials.
Why would I want to approximate your posterior if it has this shitty behavior?