Recall that confidence intervals, which are standardly taken to indicate the quality of an estimation, are often interpreted epistemically. The 95% confidence interval is often misunderstood as the range of parameter values that includes the true value with 95% probability, a so-called credal interval:  \[ P(\theta \in [\hat{\theta} - \Delta, \hat{\theta} + \Delta]) = 0.95 . \]  This interpretation is at odds with classical statistics but, as will become apparent, it can be motivated by an application of the fiducial argument. Say that we replace the integral determining the size \(\Delta\) of the confidence interval by the following:  \[ \int_{\hat{\theta}(s) - \Delta}^{\hat{\theta}(s) + \Delta} P_{\theta}(R_{\hat{\theta}(s)}) d\theta = 0.95 .\]  In words, we fix the estimator \(\hat{\theta}(s)\) and then integrate over the parameters \(\theta\) in \(P_{\theta}(R_{\hat{\theta}(s)})\), rather than assuming \(\theta^{\star}\) and then integrating over the parameters \(\tau\) in \(R_{\tau}\). Sure enough we can calculate this integral. But what ensures that we can treat the integral as a probability? Notice that it runs over a continuum of probability distributions and that, as it stands, there is no reason to think that the terms \(P_{\theta}(R_{\hat{\theta}(s)})\) add up to a proper distribution in \(\theta\).