Scott Ferson, Michael Balch, Kari Sentz, Jack Siegrist

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Computing with Confidence

Abstract

Traditional confidence intervals are useful in engineering because they offer a guarantee of statistical performance through repeated use. However, it is difficult to employ them consistently in analyses and assessments because it is not clear how to propagate them through mathematical calculations. Confidence structures (c-boxes) generalize confidence distributions and provide an interpretation by which confidence intervals at any confidence level can be specified for a parameter of interest. C-boxes can be used in calculations using the standard methods of probability bounds analysis and yield results that also admit the confidence interpretation. Thus analysts using them can now literally compute with confidence. We illustrate the calculation and use of c-boxes for some elementary inference problems and describe R functions to compute them and some Monte Carlo simulations demonstrating the coverage performance of the c-boxes and calculations based on them.

Keywords

confidence intervals, confidence structures, c-boxes, p-boxes, probability bounds analysis, binomial probability, imprecise beta model, t-distribution

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E-mail addresses

Scott Ferson		scott@ramas.com
Michael Balch		Michael.Balch.ctr@wpafb.af.mil
Kari Sentz		ksentz@lanl.gov
Jack Siegrist		jack@ramas.com