The posterior probability density provides a basis for conclusions that one might draw from the sample \(s\), and which are similar to estimations and measures for the accuracy of the estimations. For one, we can derive an expectation for the parameter \(\theta\), where we assume that \(\theta\) varies continuously:  \[ \bar{\theta} \;\; = \;\; \int_{\Theta}\, \theta P(h_{\theta} \mid s) d\theta. \]  If the model is parameterized by a convex set, which it typically is, then there will be a hypothesis \(h_{\bar{\theta}}\) in the model. This hypothesis can serve as a Bayesian estimation. In analogy to the confidence interval, we can also define a so-called credal interval or credibility interval from the posterior probability distribution: an interval of size \(2d\) around the expectation value \(\bar{\theta}\), written \([\bar{\theta} - d, \bar{\theta} + d]\), such that  \[ \int_{\bar{\theta} - d}^{\bar{\theta} + d} P(h_{\theta} \mid s) d\theta = 1-\epsilon .  \]  This range of values for \(\theta\) is such that the posterior probability of the corresponding \(h_{\theta}\) adds up to \(1-\epsilon\) of the total posterior probability.