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

TL;DR

This paper introduces a Bayesian approach combined with confidence intervals to improve amplitude estimation of sine functions, addressing biases in traditional least squares methods.

Contribution

It presents a novel method integrating Feldman-Cousins confidence intervals and Bayesian probability density functions for more accurate amplitude estimation.

Findings

Bayesian method outperforms least squares in small amplitude cases

Feldman-Cousins intervals reduce bias in amplitude estimates

Application demonstrates improved estimation accuracy

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 for small amplitudes. 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.