Amplitude estimation of a sine function based on confidence intervals and Bayes' theorem. (3rd May 2016)

• Record Type: Journal Article
• Authors: Eversmann, D.; Pretz, J.; Rosenthal, M.
• Is Part Of: Journal of instrumentation. Volume 11:Number 5(2016:May)
• Page Start: P05003
• Page End: P05003
• Publication Date: 2016-05-03
• Subjects: Analysis and statistical methods -- Data analysis -- Polarisation -- Data processing methods; Scientific apparatus and instruments -- Periodicals; 502.84
• DOI: 10.1088/1748-0221/11/05/P05003
• Languages: English
• ISSNs: 1748-0221

Abstract

Abstract: This paper discusses the amplitude estimation using data originating from a sine-like function as probability density function. If a simple least squares fit is used, a significant bias is observed if the amplitude is small compared to its error. It is shown that a proper treatment using the Feldman-Cousins algorithm of likelihood ratios allows one to construct improved confidence intervals. Using Bayes' theorem a probability density function is derived for the amplitude. It is used in an application to show that it leads to better estimates compared to a simple least squares fit.