Maximum Likelihood Methods for Two-Variable Datasets

Abstract

One of the most common tasks in the analysis of scientific data is to establish a relationship between two quantities. Many experiments feature the measurement of a quantity of interest as function of another control quantity that is varied as the experiment is performed. In this chapter we use the maximum likelihood method to determine whether a certain relationship between the two quantities is consistent with the available measurements and the best-fit parameters of the relationship. The method has a simple analytic solution for a linear function but can also be applied to more complex analytic functions.