# Learning Optimal Test Statistics in the Presence of Nuisance Parameters

arXiv: https://arxiv.org/abs/2203.13079 · HTML: https://mlsanity.com/paper/2203.13079/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2022.

## Built on by (most cited first, 4 of 4)

- [Hierarchical Neural Simulation-Based Inference Over Event Ensembles](https://mlsanity.com/paper/2306.12584/) (2023)
- [Tests for model misspecification in simulation-based inference: from local distortions to global model checks](https://mlsanity.com/paper/2412.15100/) (2024)
- [FAIR Universe HiggsML Uncertainty Dataset and Competition](https://mlsanity.com/paper/2410.02867/) (2024)
- [Likelihood-free inference with nuisance parameters through normalizing flows](https://mlsanity.com/paper/2609.10534/) (2026)

## Abstract (arXiv)

The design of optimal test statistics is a key task in frequentist statistics and for a number of scenarios optimal test statistics such as the profile-likelihood ratio are known. By turning this argument around we can find the profile likelihood ratio even in likelihood-free cases, where only samples from a simulator are available, by optimizing a test statistic within those scenarios. We propose a likelihood-free training algorithm that produces test statistics that are equivalent to the profile likelihood ratios in cases where the latter is known to be optimal.