Amplitude estimation of a sine function based on confidence intervals and Bayes' theorem

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.