Confidence intervals with a priori parameter bounds

Understand

We review the methods of constructing confidence intervals that account for a priori information about one-sided constraints on the parameter being estimated.

• We show that the so-called method of sensitivity limit yields a correct solution of the problem.
• Derived are the solutions for the cases of a continuous distribution with non-negative estimated parameter and a discrete distribution, specifically a Poisson process with background.
• For both cases, the best upper limit is constructed that accounts for the a priori information.