# Uncertain Evidence in Probabilistic Models and Stochastic Simulators

arXiv: https://arxiv.org/abs/2210.12236 · HTML: https://mlsanity.com/paper/2210.12236/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 49 references that are in the map.
- First posted on arXiv 21 Oct 2022.

## Builds on (most cited first, 10 of 10)

- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Real-time gravitational-wave science with neural posterior estimation](https://mlsanity.com/paper/2106.12594/) (2021)
- [Simulation Intelligence: Towards a New Generation of Scientific Methods](https://mlsanity.com/paper/2112.03235/) (2021)
- [Inference Compilation and Universal Probabilistic Programming](https://mlsanity.com/paper/1610.09900/) (2016)
- [A neural simulation-based inference approach for characterizing the Galactic Center γ-ray excess](https://mlsanity.com/paper/2110.06931/) (2021)
- [Probabilistic Programs with Stochastic Conditioning](https://mlsanity.com/paper/2010.00282/) (2020)
- [Efficient Probabilistic Inference in the Quest for Physics Beyond the Standard Model](https://mlsanity.com/paper/1807.07706/) (2018)
- [Probabilistic Surrogate Networks for Simulators with Unbounded Randomness](https://mlsanity.com/paper/1910.11950/) (2019)
- [Probability Update: Conditioning vs. Cross-Entropy](https://mlsanity.com/paper/1302.1543/) (2013)
- [Planning as Inference in Epidemiological Models](https://mlsanity.com/paper/2003.13221/) (2020)

## Built on by (most cited first, 5 of 5)

- [AlphaFold's Bayesian Roots in Probability Kinematics](https://mlsanity.com/paper/2505.19763/) (2025)
- [Towards More General Control of Diffusion Models Using Jeffrey Guidance](https://mlsanity.com/paper/2606.13240/) (2026)
- [Efficient Incremental Belief Updates Using Weighted Virtual Observations](https://mlsanity.com/paper/2402.06940/) (2024)
- [Position: AI for Science Should Treat Measurement-to-Dataset Pipelines as Inference Components](https://mlsanity.com/paper/2605.24558/) (2026)
- [Rethinking Soft Tokens for Parallel Decoding in Diffusion Language Models](https://mlsanity.com/paper/2609.37391/) (2026)

## Abstract (arXiv)

We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the importance of proper interpretation as it pertains to inference about latent variables. We consider a recently-proposed method "distributional evidence" as well as revisit two older methods: Jeffrey's rule and virtual evidence. We devise guidelines on how to account for uncertain evidence and we provide new insights, particularly regarding consistency. To showcase the impact of different interpretations of the same uncertain evidence, we carry out experiments in which one interpretation is defined as "correct." We then compare inference results from each different interpretation illustrating the importance of careful consideration of uncertain evidence.