New method to determine the decision threshold for low-level radioactivity measurements

Area of Science:

• Metrology and Measurement Science
• Statistical Inference
• Nuclear and Radiation Physics

Background:

• Selecting appropriate confidence intervals (one-sided vs. two-sided) is crucial for accurate statistical inference.
• Existing methods may lack a unified approach for determining optimal decision thresholds, especially for non-negative measurands.
• Low-level radioactivity measurements often involve non-negative count rates, requiring specialized statistical treatment.

Purpose of the Study:

• To develop and present a novel method for determining the optimal decision threshold.
• To facilitate the choice between one-sided and two-sided confidence intervals based on this threshold.
• To apply the method to net count rate measurements in low-level radioactivity.

Main Methods:

• Utilized the Feldman-Cousins unified approach to establish unique confidence regions for estimated parameters.
• Developed a decision threshold criterion based on this unified approach.
• Applied the method to a net count rate measurand, considering its non-negative physical constraint.

Main Results:

• Tabulated decision threshold values and detection limits for various coverage probabilities.
• Demonstrated that the proposed decision threshold effectively distinguishes the presence or absence of a physical effect.
• Provided a robust framework for statistical decision-making in radioactivity measurements.

Conclusions:

• The new decision threshold method offers a principled way to select confidence interval types.
• The Feldman-Cousins approach provides a unified basis for statistical decisions in constrained measurement scenarios.
• This method enhances the reliability of detecting physical effects in low-level radioactivity studies.