# Improving the Accuracy of Marginal Approximations in Likelihood-Free Inference via Localisation

arXiv: https://arxiv.org/abs/2207.06655 · HTML: https://mlsanity.com/paper/2207.06655/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 60 references that are in the map.
- First posted on arXiv 14 Jul 2022.

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

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [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)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (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)
- [Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks](https://mlsanity.com/paper/2112.08866/) (2021)
- [Variational methods for simulation-based inference](https://mlsanity.com/paper/2203.04176/) (2022)
- [Sequential Neural Posterior and Likelihood Approximation](https://mlsanity.com/paper/2102.06522/) (2021)
- [Truncated Marginal Neural Ratio Estimation](https://mlsanity.com/paper/2107.01214/) (2021)
- [Solving high-dimensional parameter inference: marginal posterior densities & Moment Networks](https://mlsanity.com/paper/2011.05991/) (2020)
- [ABC random forests for Bayesian parameter inference](https://mlsanity.com/paper/1605.05537/) (2016)
- [Combining probability distributions: Extending the logarithmic pooling approach](https://mlsanity.com/paper/1502.04206/) (2015)
- [Likelihood-free approximate Gibbs sampling](https://mlsanity.com/paper/1906.04347/) (2019)
- [Adaptive Gaussian Copula ABC](https://mlsanity.com/paper/1902.10704/) (2019)
- [Simulation-efficient marginal posterior estimation with swyft: stop wasting your precious time](https://mlsanity.com/paper/2011.13951/) (2020)
- [Bayesian Restricted Likelihood Methods: Conditioning on Insufficient Statistics in Bayesian Regression](https://mlsanity.com/paper/1812.07736/) (2018)
- [Component-wise approximate Bayesian computation via Gibbs-like steps](https://mlsanity.com/paper/1905.13599/) (2019)
- [Efficient Bayesian synthetic likelihood with whitening transformations](https://mlsanity.com/paper/1909.04857/) (2019)
- [Misspecification-robust likelihood-free inference in high dimensions](https://mlsanity.com/paper/2002.09377/) (2020)
- [Modularized Bayesian analyses and cutting feedback in likelihood-free inference](https://mlsanity.com/paper/2203.09782/) (2022)
- [On the Asymptotic Efficiency of Approximate Bayesian Computation Estimators](https://mlsanity.com/paper/1506.03481/) (2015)
- [Guided sequential ABC schemes for intractable Bayesian models](https://mlsanity.com/paper/2206.12235/) (2022)
- [Likelihood-free inference in high-dimensional models](https://mlsanity.com/paper/1507.08612/) (2015)
- [ABC Samplers](https://mlsanity.com/paper/1802.09650/) (2018)

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

- [Preconditioned Neural Posterior Estimation for Likelihood-free Inference](https://mlsanity.com/paper/2404.13557/) (2024)
- [Preconditioned Robust Neural Posterior Estimation for Misspecified Simulators](https://mlsanity.com/paper/2602.18004/) (2026)

## Abstract (arXiv)

Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated from, but for which the corresponding likelihood is intractable. However, common likelihood-free methods do not scale well to a large number of model parameters. A promising approach to high-dimensional likelihood-free inference involves estimating low-dimensional marginal posteriors by conditioning only on summary statistics believed to be informative for the low-dimensional component, and then combining the low-dimensional approximations in some way. In this paper, we demonstrate that such low-dimensional approximations can be surprisingly poor in practice for seemingly intuitive summary statistic choices. We describe an idealized low-dimensional summary statistic that is, in principle, suitable for marginal estimation. However, a direct approximation of the idealized choice is difficult in practice. We thus suggest an alternative approach to marginal estimation which is easier to implement and automate. Given an initial choice of low-dimensional summary statistic that might only be informative about a marginal posterior location, the new method improves performance by first crudely localising the posterior approximation using all the summary statistics to ensure global identifiability, followed by a second step that hones in on an accurate low-dimensional approximation using the low-dimensional summary statistic. We show that the posterior this approach targets can be represented as a logarithmic pool of posterior distributions based on the low-dimensional and full summary statistics, respectively. The good performance of our method is illustrated in several examples.