# Bayesian score calibration for approximate models

arXiv: https://arxiv.org/abs/2211.05357 · HTML: https://mlsanity.com/paper/2211.05357/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 68 references that are in the map.
- First posted on arXiv 10 Nov 2022.

## Builds on (most cited first, 18 of 18)

- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Return of Frustratingly Easy Domain Adaptation](https://mlsanity.com/paper/1511.05547/) (2015)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models](https://mlsanity.com/paper/1501.03291/) (2015)
- [Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation](https://mlsanity.com/paper/1605.06376/) (2016)
- [Pareto Smoothed Importance Sampling](https://mlsanity.com/paper/1507.02646/) (2015)
- [Truncated proposals for scalable and hassle-free simulation-based inference](https://mlsanity.com/paper/2210.04815/) (2022)
- [Likelihood-Free Inference with Generative Neural Networks via Scoring Rule Minimization](https://mlsanity.com/paper/2205.15784/) (2022)
- [Diagnostic tools of approximate Bayesian computation using the coverage property](https://mlsanity.com/paper/1301.3166/) (2013)
- [Adaptive, delayed-acceptance MCMC for targets with expensive likelihoods](https://mlsanity.com/paper/1509.00172/) (2015)
- [Recalibration: A post-processing method for approximate Bayesian computation](https://mlsanity.com/paper/1704.06374/) (2017)
- [Spectral Subsampling MCMC for Stationary Time Series](https://mlsanity.com/paper/1910.13627/) (2019)
- [Accelerating sequential Monte Carlo with surrogate likelihoods](https://mlsanity.com/paper/2009.03699/) (2020)
- [An Efficient Workflow for Modelling High-Dimensional Spatial Extremes](https://mlsanity.com/paper/2210.00760/) (2022)
- [Calibration procedures for approximate Bayesian credible sets](https://mlsanity.com/paper/1810.06433/) (2018)

## Built on by (most cited first, 2 of 2)

- [Misspecification-robust Sequential Neural Likelihood for Simulation-based Inference](https://mlsanity.com/paper/2301.13368/) (2023)
- [CP4SBI: Local Conformal Calibration of Credible Sets in Simulation-Based Inference](https://mlsanity.com/paper/2508.17077/) (2025)

## Abstract (arXiv)

Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often intractable and model simulation may be computationally burdensome. Fortunately, in many of these situations it is possible to adopt a surrogate model or approximate likelihood function. It may be convenient to conduct Bayesian inference directly with a surrogate, but this can result in a posterior with poor uncertainty quantification. In this paper, we propose a new method for adjusting approximate posterior samples to reduce bias and improve posterior coverage properties. We do this by optimizing a transformation of the approximate posterior, the result of which maximizes a scoring rule. Our approach requires only a (fixed) small number of complex model simulations and is numerically stable. We develop supporting theory for our method and demonstrate beneficial corrections to approximate posteriors across several examples of increasing complexity.