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Simulation based inference (SBI) methods enable the estimation of posterior distributions when the likelihood function is intractable, but where model simulation is feasible. Popular neural approaches to SBI are the neural posterior…

Machine Learning · Statistics 2024-04-23 Xiaoyu Wang , Ryan P. Kelly , David J. Warne , Christopher Drovandi

Generative models and those with computationally intractable likelihoods are widely used to describe complex systems in the natural sciences, social sciences, and engineering. Fitting these models to data requires likelihood-free inference…

Methodology · Statistics 2025-12-04 Rui Zhang , Oksana A. Chkrebtii , Dongbin Xiu

Modern simulation-based inference techniques use neural networks to solve inverse problems efficiently. One notable strategy is neural posterior estimation (NPE), wherein a neural network parameterizes a distribution to approximate the…

Instrumentation and Methods for Astrophysics · Physics 2024-03-06 Alex Kolmus , Justin Janquart , Tomasz Baka , Twan van Laarhoven , Chris Van Den Broeck , Tom Heskes

Accurate null depth retrieval is critical in nulling interferometry. However, achieving accurate null depth calibration is challenging due to various noise sources, instrumental imperfections, and the complexity of real observational…

Instrumentation and Methods for Astrophysics · Physics 2025-11-14 Baoyi Zeng , Marc-Antoine Martinod , Denis Defrère

Bayesian inference without the likelihood evaluation, or likelihood-free inference, has been a key research topic in simulation studies for gaining quantitatively validated simulation models on real-world datasets. As the likelihood…

Methodology · Statistics 2022-11-07 Dongjun Kim , Kyungwoo Song , YoonYeong Kim , Yongjin Shin , Wanmo Kang , Il-Chul Moon , Weonyoung Joo

We introduce Sequential Neural Posterior Score Estimation (SNPSE), a score-based method for Bayesian inference in simulator-based models. Our method, inspired by the remarkable success of score-based methods in generative modelling,…

Machine Learning · Statistics 2024-06-04 Louis Sharrock , Jack Simons , Song Liu , Mark Beaumont

Diagnosing the internal state of Li-ion batteries is critical for battery research, operation of real-world systems, and prognostic evaluation of remaining lifetime. By using physics-based models to perform probabilistic parameter…

Data Analysis, Statistics and Probability · Physics 2026-04-06 Malik Hassanaly , Corey R. Randall , Peter J. Weddle , Paul J. Gasper , Conlain Kelly , Tanvir R. Tanim , Kandler Smith

We present Sequential Neural Likelihood (SNL), a new method for Bayesian inference in simulator models, where the likelihood is intractable but simulating data from the model is possible. SNL trains an autoregressive flow on simulated data…

Machine Learning · Statistics 2019-01-23 George Papamakarios , David C. Sterratt , Iain Murray

Simulation-Based Inference (SBI) is a promising Bayesian inference framework that alleviates the need for analytic likelihoods to estimate posterior distributions. Recent advances using neural density estimators in SBI algorithms have…

Instrumentation and Methods for Astrophysics · Physics 2022-07-13 Justine Zeghal , François Lanusse , Alexandre Boucaud , Benjamin Remy , Eric Aubourg

Neural posterior estimation (NPE) and neural likelihood estimation (NLE) are machine learning approaches that provide accurate posterior, and likelihood, approximations in complex modeling scenarios, and in situations where conducting…

Machine Learning · Statistics 2024-11-20 David T. Frazier , Ryan Kelly , Christopher Drovandi , David J. Warne

Neural Posterior Estimation (NPE) enables rapid parameter inference for complex simulators with intractable likelihoods. NPE trains an inference network to estimate a probability density over parameters given data, typically assumed to be…

Machine Learning · Computer Science 2026-05-14 Jan Boelts , Cornelius Schröder , Jonas Beck , Jakob H. Macke , Michael Deistler , Daniel Gedon

Simulation-based inference (SBI) with neural posterior estimation (NPE) provides rapid X-ray spectral fitting in both Gaussian and Poisson regimes by learning approximate parameter posteriors from simulations. We investigate auto-encoders…

Instrumentation and Methods for Astrophysics · Physics 2026-04-22 Didier Barret , Simon Dupourqué

Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a…

We present Causal Posterior Estimation (CPE), a novel method for Bayesian inference in simulator models, i.e., models where the evaluation of the likelihood function is intractable or too computationally expensive, but where one can…

Machine Learning · Computer Science 2025-05-28 Simon Dirmeier , Antonietta Mira

Bayesian inference for complex models with an intractable likelihood can be tackled using algorithms performing many calls to computer simulators. These approaches are collectively known as "simulation-based inference" (SBI). Recent SBI…

Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…

Computation · Statistics 2026-01-09 Elliot Maceda , Emily C. Hector , Amanda Lenzi , Brian J. Reich

Simulation-based inference (SBI) offers a flexible and general approach to performing Bayesian inference: In SBI, a neural network is trained on synthetic data simulated from a model and used to rapidly infer posterior distributions for…

Machine Learning · Computer Science 2025-10-28 Julius Vetter , Manuel Gloeckler , Daniel Gedon , Jakob H. Macke

We present Sequential Neural Variational Inference (SNVI), an approach to perform Bayesian inference in models with intractable likelihoods. SNVI combines likelihood-estimation (or likelihood-ratio-estimation) with variational inference to…

Machine Learning · Statistics 2022-10-20 Manuel Glöckler , Michael Deistler , Jakob H. Macke

Simulation-Based Inference (SBI) is a common name for an emerging family of approaches that infer the model parameters when the likelihood is intractable. Existing SBI methods either approximate the likelihood, such as Approximate Bayesian…

Machine Learning · Computer Science 2023-11-29 Theo Gruner , Boris Belousov , Fabio Muratore , Daniel Palenicek , Jan Peters

Simulation-based inference with neural posterior estimation (NPE) often yields overconfident and unreliable posteriors under limited simulation budgets. To address this, we propose DRO-NPE, a distributionally robust approach that replaces…

Machine Learning · Statistics 2026-05-28 William Laplante , Yuga Hikida , Charita Dellaporta , François-Xavier Briol , Ayush Bharti
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