On the Binomial Confidence Interval and Probabilistic Robust Control

TL;DR

This paper clarifies that the Clopper-Pearson confidence interval, often considered exact in control theory, is actually conservative, prompting the development of improved methods for probabilistic robustness analysis.

Contribution

The paper analytically demonstrates the conservatism of the Clopper-Pearson interval in control applications and advocates for better confidence interval methods.

Findings

Clopper-Pearson interval is conservative in probabilistic control.

Analytic results quantify the extent of conservatism.

Encourages development of improved confidence interval methods.

Abstract

The Clopper-Pearson confidence interval has ever been documented as an exact approach in some statistics literature. More recently, such approach of interval estimation has been introduced to probabilistic control theory and has been referred as non-conservative in control community. In this note, we clarify the fact that the so-called exact approach is actually conservative. In particular, we derive analytic results demonstrating the extent of conservatism in the context of probabilistic robustness analysis. This investigation encourages seeking better methods of confidence interval construction for robust control purpose.