A method of maximum likelihood fit to data with non-uniform efficiencies

TL;DR

This paper introduces a maximum likelihood fitting method that accounts for non-uniform efficiencies by using efficiency as a weight, providing unbiased parameter estimates and reducing computational resources when the distribution can be normalized analytically.

Contribution

It presents a novel maximum likelihood approach that incorporates efficiency as a weight without altering the probability distribution, improving estimation accuracy and efficiency.

Findings

The method yields unbiased parameter estimates.

It reduces computational resources when the distribution is analytically normalizable.

Pseudo-experiments validate the effectiveness of the approach.

Abstract

Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution function is kept unaffected by the efficiency. A brief proof and pseudo-experiment studies suggest that this method gives unbiased estimation of parameters. For cases where the probability distribution function can be normalized analytically, this method significant reduces the usage of computing resources.