# Amortized Simulation-Based Frequentist Inference for Tractable and Intractable Likelihoods

arXiv: https://arxiv.org/abs/2306.07769 · HTML: https://mlsanity.com/paper/2306.07769/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 12 references that are in the map.
- First posted on arXiv 13 Jun 2023.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)

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

- [Trustworthy scientific inference with generative models](https://mlsanity.com/paper/2508.02602/) (2025)
- [Modeling Sampling Distributions of Test Statistics with Autograd](https://mlsanity.com/paper/2405.02488/) (2024)
- [Amortized Inference for Sampling Distributions Where the Bootstrap Fails](https://mlsanity.com/paper/2607.16666/) (2026)
- [Likelihood-free inference with nuisance parameters through normalizing flows](https://mlsanity.com/paper/2609.10534/) (2026)

## Abstract (arXiv)

High-fidelity simulators that connect theoretical models with observations are indispensable tools in many sciences. When coupled with machine learning, a simulator makes it possible to infer the parameters of a theoretical model directly from real and simulated observations without explicit use of the likelihood function. This is of particular interest when the latter is intractable. In this work, we introduce a simple extension of the recently proposed likelihood-free frequentist inference (LF2I) approach that has some computational advantages. Like LF2I, this extension yields provably valid confidence sets in parameter inference problems in which a high-fidelity simulator is available. The utility of our algorithm is illustrated by applying it to three pedagogically interesting examples: the first is from cosmology, the second from high-energy physics and astronomy, both with tractable likelihoods, while the third, with an intractable likelihood, is from epidemiology.