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.

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