Application of Conditioning to the Gaussian-with-Boundary Problem in the Unified Approach to Confidence Intervals

TL;DR

This paper explores applying a conditioning technique to the Gaussian-with-boundary problem within the unified approach for confidence intervals, revealing significant shifts in the confidence belt that may be undesirable.

Contribution

It extends the conditioning method suggested by Roe and Woodroofe to Gaussian errors with boundaries, analyzing its effects on confidence belt boundaries.

Findings

Significant shift in the upper confidence belt curve.

Unintended significant movement of the lower confidence belt curve.

Conditioning may have undesirable effects on confidence interval boundaries.

Abstract

Roe and Woodroofe (RW) have suggested that certain conditional probabilities be incorporated into the ``unified approach'' for constructing confidence intervals, previously described by Feldman and Cousins (FC). RW illustrated this conditioning technique using one of the two prototype problems in the FC paper, that of Poisson processes with background. The main effect was on the upper curve in the confidence belt. In this paper, we attempt to apply this style of conditioning to the other prototype problem, that of Gaussian errors with a bounded physical region. We find that the lower curve on the confidence belt is also moved significantly, in an undesirable manner.