I'm looking for some advice and particularly literature pointers for a
question about the Bayesian stance. I'm interested in what approaches
are suggested for handling the case where one's prior is qualitatively
wrong.
For example, imagine that I have chosen a normal distribution for a
random variable, and when the observations come back, they are bimodal.
What does the Bayesian philosophy say about cases like this?
Unless I have previously considered this possibility, I can't sensibly
update my prior to a posterior, and as I understand it, is critical that
my prior be independent of the observations, so revising my prior before
I compute the posterior isn't kosher.
I'm sure that there must be a literature on this in statistics and
philosophy, but I don't know how to find it. Maybe there's a jargon
term that I just don't know.
Thanks!
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