# Credible intervals for bounded parameters

Hi! I’m fitting a mixture model with mixture components being two VonMises distributions and a one uniform circular distribution. The posterior for the uniform distribution weight (fraction in the mixture) looks almost flat from ~0% to ~40%, which seems correct looking at the data histogram - it can be fit with either two wider peaks or two narrower peaks with a uniform component.
But I’m not sure how to proceed with the credible interval for this parameter (uniform distribution weight). Of course, if I just compute the 5 and 95 percentiles of the posterior, this interval will never include 0 (its lower boundary). However intuitively I would expect 0 to be in the credible interval if the model cannot distinguish between the parameter being zero and not zero.
Any thoughts on how to handle this statistically correctly? We can just take the credible interval to be from 0 to 95 percentile of posterior in this case, but this is just some ad-hoc treatment.

It’s ok to choose the most suitable definition of a credible region for your problem. The Wikipedia entry explains it well. Your latter suggestion sounds preferable for your case, though it would be a 95% interval.

An obvious situation where your choice matters is when your posterior distribution is multimodel.

(picture nabbed from here)

While both intervals contain 90% of the posterior density, forming two intervals is usually preferable, since
choosing the single interval in the picture covers a region of negligible posterior density.

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