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I'm working with a general bayesian information criteria to determine if this data exhibits a bimodal, trimodal, quadmodal etc. My existing BIC exhibits clear trimodality, but I'd like a hypothesis test of sorts.

How can I determine the probability that this model is true?

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    $\begingroup$ You could consider the relationship with AIC and this relationship with the chi-square fitting (under the corresponding assumptions, of course). If you want to use probabilities, then I think Bayes factors would be more suitable, but then you need to choose a prior for the parameters. $\endgroup$ – user10525 Jul 20 '12 at 16:29
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    $\begingroup$ Models are never true. They are intended to be useful approximations to reality. That is why George Box is often quoted for his wise comment that is something like "No model is correct but some are useful." $\endgroup$ – Michael R. Chernick Jul 20 '12 at 16:48
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    $\begingroup$ BIC is not directly Bayesian so you cannot derive a test from it. More positively, as Procrastinator said, you should use Bayes factors, i.e. ratios of marginal distributions for the different models. Since you use BIC, you already had priors on the parameters, right? $\endgroup$ – Xi'an Jul 23 '12 at 7:02

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