Bayesian inference on a squared quantity

• Published in: Measurement : journal of the International Measurement Confederation Vol. 48; pp. 13 - 20
• Main Author: Carobbi, Carlo
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2014
• Subjects: Bayesian analysis; Bayesian inference; Complexity; Defects; Derivation; Estimators; Frequentist inference; Mathematical analysis; Measurement uncertainty; Method of moments; Method of moments estimators; Noncentral chi-squared distribution; Paradoxes; Noncentral chi-squared distribution; Frequentist inference; Bayesian inference; Measurement uncertainty; Method of moments estimators
• ISSN: 0263-2241; 1873-412X
• DOI: 10.1016/j.measurement.2013.10.034

•Bayesian estimator of noncentrality parameter of noncentral χ2 pdf is derived.•The analytical insightful derivation reveals how the Bayesian estimator works.•Bayesian estimator outperforms frequentist one based on method of moments.•Paradox presented in a previously published work is resolved. It is here derived the Bayesian estimator of the noncentrality parameter of the noncentral chi-square distribution. The corresponding frequentist estimator, based on the method of moments, is also derived and its performance is compared with the Bayesian one. The Bayesian estimator is obtained through an analytical derivation which provides insight into the way the estimator works. Reference is also made here to a previously published work on a similar subject by Attivissimo et al. (2012) [1] in order to resolve the paradox there presented. Some defects of the analysis performed in the referenced work are identified and carefully examined. The superiority of the Bayesian estimator is demonstrated although achieved at the price of a greater complexity.