I have a particular semiparametric model which I'm fitting via MCMC. One of the model parameters I have "semiparametric'ed" away (say $\alpha$) is known to lie between two other parameters, $\theta_1$ and $\theta_2$. Since I have a series of samples $(\theta_1^t, \theta_2^t)$ I also have a series of interval estimates for $\alpha$. What is a reasonable way to summarize these? I can think of doing something like putting down a grid and just recording for each gridpoint whether each sample covers it or not. But I worry about efficiency since I don't have a great sense of what a plausible range is, and I actually have hundreds to thousands of $\alpha$'s.
(I'm also welcoming retags, since I can't seem to find any I like...)