Inference about constrained parameters using the elastic belief method

Statistical inference about unknown parameter values that have known constraints is a challenging problem for both frequentist and Bayesian methods. As an alternative, inferential models created with the weak belief method can generate inferential results with desirable frequency properties for constrained parameter problems. To accomplish this, we propose an extension of weak belief called the elastic belief method. Compared to an existing rule for conditioning on constraint information, the elastic belief method produces more efficient probabilistic inference while maintaining desirable frequency properties. The application of this new method is demonstrated in two well-studied examples: inference about a nonnegative quantity measured with Gaussian error and inference about the signal rate of a Poisson count with a known background rate. Compared to several previous interval-forming methods for the constrained Poisson signal rate, the new method gives an interval with better coverage probability or a simpler construction. More importantly, the inferential model provides a post-data predictive measure of uncertainty about the unknown parameter value that is not inherent in other interval-forming methods.

► We introduce the elastic belief method for inference about constrained parameters. ► An existing conditioning rule is credible for inference about constrained parameters. ► The elastic belief method is more efficient than the existing conditioning rule. ► We demonstrate the elastic belief method with Gaussian and Poisson examples.