I guess it depends on what the “correct direction” is thought to be. From the reasoning quoted in my first post, it could be the case that as the study result becomes larger the posterior expectation should actually reduce. It’s not inconceivable that as we saw the estimate go to infinity, we should start reasoning that the study is so ridiculous as to be uninformative and so not the posterior update becomes smaller. But I don’t know. What you say seems to suggest that Bayesian reasoning could only do that for rather specific choices of likelihood functions, which is interesting.
I guess it depends on what the “correct direction” is thought to be. From the reasoning quoted in my first post, it could be the case that as the study result becomes larger the posterior expectation should actually reduce. It’s not inconceivable that as we saw the estimate go to infinity, we should start reasoning that the study is so ridiculous as to be uninformative and so not the posterior update becomes smaller. But I don’t know. What you say seems to suggest that Bayesian reasoning could only do that for rather specific choices of likelihood functions, which is interesting.