Avoiding biases in binned fits

TL;DR

This paper identifies biases in binned maximum likelihood fits caused by evaluating probabilities at bin centers and introduces a new RooFit PDF class that removes these biases, improving accuracy in analyzing large datasets.

Contribution

A new RooFit PDF class is proposed that eliminates biases in binned likelihood fits for strongly curved PDFs, enhancing analysis accuracy.

Findings

Demonstrated biases in traditional binned fits with real-world examples

Introduced a bias-free PDF class for RooFit

Discussed performance and physics implications of the new class

Abstract

Binned maximum likelihood fits are an attractive option when analysing large datasets, but require care when computing likelihoods of continuous PDFs in bins. For many years the widely used statistical modelling package RooFit evaluated probabilities at the bin centre, leading to significant biases for strongly curved probability density functions. We demonstrate the biases with real-world examples, and introduce a PDF class to RooFit that removes these biases. The physics and computation performance of this new class are discussed.