Thanks, but the flat improper prior isn't really appropriate for this
case. In this case I have a bunch of observations in a first research
study that are very much normally distributed with obvious peaks.
I'm looking now at an attempt to replicate this first study, where the
replication didn't really succeed, in the sense that in some cases I see
a bimodal shape in the distribution.
So the uniform prior would be to pretend that I didn't have information
I really do have, and would also have the side-effect of making the new
data seem unsurprising (i.e., have less information content), in a way
that it is not....
I am starting to suspect "zooming out" ("going meta") and treating the
prior in a second order way, as effectively the expectation over a model
that considers other qualitative models is the right thing to do here.
But that said I don't see any principled way to create this hierarchical
model.
Best,
r
On 23 Feb 2018, at 14:55, Richard E Neapolitan wrote:
Hi Robert,
I think it is more a frequentist thing to be dogmatic about rules like
keeping the prior independent of the observations. Regardless, I would
suggest using the flat improper prior. It has no peak(s). So you are
not assuming the distribution is unimodal. I discuss it in my text
Learning Bayesian networks, and in Chapter 2 of the following:
http://bayanbox.ir/view/2736375761831808090/Dawn-E.-Holmes-Lakhmi-C.-Jain-Innovations-in-Ba.pdf#page=15
Best,
Rich
On 2/23/2018 12:48 PM, Robert Goldman wrote:
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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