# Given a marginal posterior distribution, when should I report an upper limit on the parameter?

I've been utilizing MCMC in the analysis of $\gamma$-ray spectra. For many of my model-parameters, the marginal posterior distributions, $p( \theta_i |X)$ where ($\theta_i\in(0,1]$), are normal distributions. Reporting values for these parameters is pretty straightforward. There are cases, however, where the parameters are small. The marginal posterior distributions for these are positively skewed, with a mode close to the zero. Is there a rule for when to report an upper-limit on such a parameter? My solution so far has been to calculate the highest posterior density interval (HPD), figuring that if the HPD covers the lowest allowable interval (starting at zero), then an upper-limit is warranted. This doesn't seem to be good practice.

I would appreciate any insight here. Statistics isn't my first language, so I apologize for any confusion.

• Reporting the HPD regions is a reasonable proposal, assuming it is easy to find the marginal HPD's. In general, I would not know how to do this. – Xi'an Nov 30 '15 at 19:45