It is crucial that we can provide an unproblematic frequentist interpretation of the event that \(\hat{\theta} \in [\theta^{\star} - \Delta, \theta^{\star} + \Delta]\), under the assumption of the true distribution. In a series of estimations, the fraction of times in which the estimator \(\hat{\theta}\) is further away from \(\theta^{\star}\) than \(\Delta\), and hence outside this interval, will tend to 5%. The smaller this region, the more reliable the estimate.  Note that this interval is defined in terms of the unknown true value \(\theta^{\star}\). However, especially if the size of the interval \(2 \Delta\) is independent of the true parameter \(\theta^{\star}\), it is tempting to associate the 95% confidence interval with the frequency with which the true value lies within a range of \(\Delta\) around the estimate \(\hat{\theta}\).  Below we come back to this interpretation.