# Expert-elicitation method for non-parametric joint priors using normalizing flows

arXiv: https://arxiv.org/abs/2411.15826 · HTML: https://mlsanity.com/paper/2411.15826/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 89 references that are in the map.
- First posted on arXiv 24 Nov 2024.

## Builds on (most cited first, 27 of 27)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [End-to-End Multi-Task Learning with Attention](https://mlsanity.com/paper/1803.10704/) (2018)
- [Multi-Task Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2009.09796/) (2020)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [TensorFlow Distributions](https://mlsanity.com/paper/1711.10604/) (2017)
- [Multi-Objective Loss Balancing for Physics-Informed Deep Learning](https://mlsanity.com/paper/2110.09813/) (2021)
- [Implicit Reparameterization Gradients](https://mlsanity.com/paper/1805.08498/) (2018)
- [Bayesian Workflow](https://mlsanity.com/paper/2011.01808/) (2020)
- [BayesFlow: Amortized Bayesian Workflows With Neural Networks](https://mlsanity.com/paper/2306.16015/) (2023)
- [Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorial](https://mlsanity.com/paper/2305.04933/) (2023)
- [Visualization in Bayesian workflow](https://mlsanity.com/paper/1709.01449/) (2017)
- [Prior knowledge elicitation: The past, present, and future](https://mlsanity.com/paper/2112.01380/) (2021)
- [The prior can generally only be understood in the context of the likelihood](https://mlsanity.com/paper/1708.07487/) (2017)
- [Penalising model component complexity: A principled, practical approach to constructing priors](https://mlsanity.com/paper/1403.4630/) (2014)
- [Sensitivity analysis for Bayesian hierarchical models](https://mlsanity.com/paper/1312.4797/) (2013)
- [Methods for Eliciting Informative Prior Distributions: A Critical Review](https://mlsanity.com/paper/2112.07090/) (2021)
- [Flexible Prior Elicitation via the Prior Predictive Distribution](https://mlsanity.com/paper/2002.09868/) (2020)
- [Translating predictive distributions into informative priors](https://mlsanity.com/paper/2303.08528/) (2023)
- [Simulation-Based Prior Knowledge Elicitation for Parametric Bayesian Models](https://mlsanity.com/paper/2308.11672/) (2023)

## Built on by (most cited first, 1 of 1)

- [Score-Based Density Estimation from Pairwise Comparisons](https://mlsanity.com/paper/2510.09146/) (2025)

## Abstract (arXiv)

We propose an expert-elicitation method for learning non-parametric joint prior distributions using normalizing flows. Normalizing flows are a class of generative models that enable exact, single-step density evaluation and can capture complex density functions through specialized deep neural networks. Building on our previously introduced simulation-based framework, we adapt and extend the methodology to accommodate non-parametric joint priors. Our framework thus supports the development of elicitation methods for learning both parametric and non-parametric priors, as well as independent or joint priors for model parameters. To evaluate the performance of the proposed method, we perform four simulation studies and present an evaluation pipeline that incorporates diagnostics and additional evaluation tools to support decision-making at each stage of the elicitation process.