Coverage probability of credible intervals if we take Bayesian model literally Let's say I have a Bayesian model with a proper prior $\pi$, likelihood $L$, data distribution $p(x|\theta)$ (assume $\theta$ is a scalar) and the vector of sample values $x$:
$$p(\theta|x) = \frac{\pi(\theta)L(\theta|x)}{p(x)}$$
If I took my model seriously as a hierarchical description of the data generating process,
$$ \theta \sim \pi$$
$$ x\sim p(\theta)$$
then how often would a 95% credibility interval (constructed from the posterior distribution) contain the generated $\theta$? 
Also, would this coverage statement be conditional on the collected data, or would it be unconditional and hence vulnerable to the usual relevant subset arguments directed at confidence intervals?
 A: As there is no generally accepted / unique way to specify (uninformative) priors, and as different priors will lead to a different credible intervals, it seems obvious that the coverage of Bayesian CIs is not fixed, but will depend on the prior that you choose, in relation to the "true" parameter values. 
It will generally also depend on the data, in particular on the size of the data - in a low data situation, the prior dominates the CI, with the mentioned consequences of a strong prior influence on the coverage. When moving to large data / asymptotics, the Bayesian CI and the frequentist CI will usually become increasingly similar, including their coverage properties. 
A: I asked a similar question:
Methods for testing a Bayesian method's software implementation and got this answer from @jaradniemi:

Bayesians don't lose the relative frequency-based interpretation of
  probability. In particular, if you define this procedure:
  
  
*
  
*simulate from the prior,
  
*then simulate from the model using those
  values from the prior, and
  
*estimate the parameters using the same
  prior.
  
  
  Then your credible intervals should have the appropriate
  frequentist coverage, i.e. 95% intervals should include the true
  parameter in 95% of your analyses, over repeated replicates of the
  procedure.

I think he's right. You're allowed to stray from the relative-frequency concept of probability as a bayesian, but you don't automatically lose it. And if you're generating data, you definitely haven't lost it.
Regarding your question about conditional vs unconditional, while each individual credible interval would be conditional on the data, the relative-frequency based coverage would be unconditional since you're averaging over draws of the data. You can also search the web for "frequentist properties of bayesian methods" and get quite a few hits.
