# Simulation-Based Prior Knowledge Elicitation for Parametric Bayesian Models

arXiv: https://arxiv.org/abs/2308.11672 · HTML: https://mlsanity.com/paper/2308.11672/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 69 references that are in the map.
- First posted on arXiv 22 Aug 2023.

## Builds on (most cited first, 24 of 24)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [End-to-End Multi-Task Learning with Attention](https://mlsanity.com/paper/1803.10704/) (2018)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Multi-Task Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2009.09796/) (2020)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [A* Sampling](https://mlsanity.com/paper/1411.0030/) (2014)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [Implicit Reparameterization Gradients](https://mlsanity.com/paper/1805.08498/) (2018)
- [Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks](https://mlsanity.com/paper/2112.08866/) (2021)
- [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)
- [Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy](https://mlsanity.com/paper/2209.02439/) (2022)
- [A Tutorial on Parametric Variational Inference](https://mlsanity.com/paper/2301.01236/) (2023)
- [Reparameterization trick for discrete variables](https://mlsanity.com/paper/1611.01239/) (2016)
- [Methods for Eliciting Informative Prior Distributions: A Critical Review](https://mlsanity.com/paper/2112.07090/) (2021)
- [Intuitive Joint Priors for Bayesian Linear Multilevel Models: The R2D2M2 prior](https://mlsanity.com/paper/2208.07132/) (2022)
- [Online simulator-based experimental design for cognitive model selection](https://mlsanity.com/paper/2303.02227/) (2023)
- [Flexible Prior Elicitation via the Prior Predictive Distribution](https://mlsanity.com/paper/2002.09868/) (2020)
- [Generalized Gumbel-Softmax Gradient Estimator for Generic Discrete Random Variables](https://mlsanity.com/paper/2003.01847/) (2020)
- [Translating predictive distributions into informative priors](https://mlsanity.com/paper/2303.08528/) (2023)
- [Beyond Convergence: Identifiability of Machine Learning and Deep Learning Models](https://mlsanity.com/paper/2307.11332/) (2023)

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

- [Expert-elicitation method for non-parametric joint priors using normalizing flows](https://mlsanity.com/paper/2411.15826/) (2024)

## Abstract (arXiv)

A central characteristic of Bayesian statistics is the ability to consistently incorporate prior knowledge into various modeling processes. In this paper, we focus on translating domain expert knowledge into corresponding prior distributions over model parameters, a process known as prior elicitation. Expert knowledge can manifest itself in diverse formats, including information about raw data, summary statistics, or model parameters. A major challenge for existing elicitation methods is how to effectively utilize all of these different formats in order to formulate prior distributions that align with the expert's expectations, regardless of the model structure. To address these challenges, we develop a simulation-based elicitation method that can learn the hyperparameters of potentially any parametric prior distribution from a wide spectrum of expert knowledge using stochastic gradient descent. We validate the effectiveness and robustness of our elicitation method in four representative case studies covering linear models, generalized linear models, and hierarchical models. Our results support the claim that our method is largely independent of the underlying model structure and adaptable to various elicitation techniques, including quantile-based, moment-based, and histogram-based methods.