Confidence bound (${\mathrm{Pr}}_{\theta }\{L\le \theta \}\ge 1-\alpha$)

A lower confidence bound $L$ gives a one-sided confidence interval with the displayed coverage requirement for every admissible parameter. An upper bound $U$ instead satisfies ${\mathrm{Pr}}_{\theta }\{\theta \le U\}\ge 1-\alpha$. Coverage is a repeated-sampling property; it does not assign a posterior probability to the fixed parameter.