Suppose we have a random sample $X_1, ..., X_n$ where $X \sim$ Expo$(\theta)$ (here $\theta$ is the rate). We're studying the Bayes estimator of $\theta$ and its properties. For a Gamma$(\alpha, \beta)$ ($\beta$ as scale) prior, I found the posterior distribution to be $$\text{Gamma}(\alpha + n, \left( \sum X_i + 1 / \beta \right)^{-1})$$ and consequently the Bayes estimator as $$T^{B}(X_1, ..., X_n) = \frac{\alpha + n}{\sum X_i + 1 / \beta}. $$
Now I'm tasked to find a credible region for $\theta$, but I'm quite confused on how to find this. Initially I thought this could just be the quantiles of our posterior distribution, but looking a bit around online, this doesn't seem to be the case...