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• A Complete Recipe for Stochastic Gradient MCMC - An Ma, Tianqi Chen, Emily B. Fox* — Provides a unifying framework showing that SGLD, SGHMC, and other SG-MCMC variants are all special cases of continuous Markov processes parameterized by two matrices, and introduces new samplers like SGRHMC within this framework.
• Normalizing Flows for Probabilistic Modeling and Inference - based inference.
• Variational Inference with Normalizing Flows - field assumption that limits standard VI and enabling arbitrarily complex approximate posteriors.
• Score-Based Generative Modeling through Stochastic Differential Equations - Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole* — Unifies score matching and diffusion models as continuous-time SDEs that gradually corrupt data into noise and reverse the process via learned score functions; provides the theoretical foundation for using diffusion models as priors in Bayesian inverse problems.
• Diffusion Posterior Sampling for General Noisy Inverse Problems - constrained gradients to handle both linear and nonlinear forward models with noise.
• Bayesian Learning via Stochastic Gradient Langevin Dynamics - batch MCMC.
• The Frontier of Simulation-Based Inference - based likelihood-free inference; surveys how neural density estimators, classifiers, and ratio estimators replace the rejection/tolerance mechanisms of ABC with learned surrogates.
• Benchmarking Simulation-Based Inference - Matthis Lueckmann, Jan Boelts, David Greenberg, Pedro Goncalves, Jakob Macke* — Systematic comparison of NPE, NLE, NRE and classical ABC on standardized tasks; finds that neural methods consistently outperform ABC but no single algorithm dominates, and that sequential variants improve sample efficiency.
• Automatic Posterior Transformation for Likelihood-Free Inference
• Sequential Neural Likelihood
• Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation - tolerance that limits ABC and requiring orders of magnitude fewer simulations.
• Approximating Likelihood Ratios with Calibrated Discriminative Classifiers - data pairs, whose output directly estimates the likelihood ratio — avoids density estimation entirely, requiring only a binary classification objective, and is well-suited to hypothesis testing.
• A Conceptual Introduction to Hamiltonian Monte Carlo
• Bayesian Methods for Hackers - Pilon (the main author)*
• Bayesian Data Analysis
• Bayesian Workflow - Christian Bürkner, Martin Modrák*
• Equation of State Calculations by Fast Computing Machines
• Monte Carlo Sampling Methods Using Markov Chains and Their Applications
• Understanding the Metropolis-Hastings Algorithm
• The Geometric Foundations of Hamiltonian Monte Carlo
• The No-U-Turn Sampler: Adaptively Setting Path Lengthsin Hamiltonian Monte Carlo
• Approximate Bayesian Computation in Population Genetics
• Markov chain Monte Carlo without likelihoods
• Sequential Monte Carlo without likelihoods
• Non-linear regression models for Approximate Bayesian Computation
• Likelihood-free Markov chain Monte Carlo
• Approximate Bayesian Computation(ABC) in practice
• Hamiltonian ABC
• Reliable ABC model choice via random forests - Michel Marin, Arnaud Estoup, Jean-Marie Cornuet, Mathieu Gautier, Christian P. Robert*
• Bayesian parameter estimation viavariational methods
• The Variational Gaussian Approximation Revisited
• Doubly Stochastic Variational Bayes for non-Conjugate Inference - Gredilla*
• Variational Inference: A Review for Statisticians
• Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm
• Gaussian Processes for Machine Learning
• The Well-Calibrated Bayesian
• Transforming Classifier Scores into Accurate Multiclass Probability Estimates
• Predicting Good Probabilities With Supervised Learning - Mizil, Rich Caruana*
• Nearly-Isotonic Regression
• Beta calibration: a well-founded and easily implemented improvement on logistic calibration for binary classifiers
• Verified Uncertainty Calibration
• Improving Regression Uncertainty Estimates with an Empirical Prior
• BAT.jl
• PyMC3 - devs/pymc4)
• Monte Carlo Sampling Methods Using Markov Chains and Their Applications
• The No-U-Turn Sampler: Adaptively Setting Path Lengthsin Hamiltonian Monte Carlo
• Approximate Bayesian Computation(ABC) in practice
• Bayesian parameter estimation viavariational methods
• Doubly Stochastic Variational Bayes for non-Conjugate Inference - Gredilla*
• Gaussian Processes for Machine Learning
• The Well-Calibrated Bayesian
• Bayesian Neural Networks
• Stochastic Gradient Hamiltonian Monte Carlo - walk behavior of SGLD.
• Sequential Monte Carlo Methods in Practice - space models where MCMC would require re-running from scratch.
• Sequential Monte Carlo Samplers
• An Introduction to Sequential Monte Carlo - Kac formalism) and practice of SMC, including waste-free SMC and connections to tempering strategies used in modern samplers.
• Advances in Variational Inference - conjugate models), accurate VI (beyond mean-field, including normalizing flows), and amortized VI (inference networks).
• Model-Informed Flows for Bayesian Inference - Informed Flows that deliver tighter posteriors for hierarchical Bayesian models.
• Expectation Propagation for Approximate Bayesian Inference - density filtering and loopy belief propagation; often more accurate than the Laplace approximation (below) and variational Bayes at comparable cost.
• Expectation Propagation as a Way of Life
• A Practical Bayesian Framework for Backpropagation Networks - order Taylor expansion (Laplace approximation) around the MAP estimate to approximate the posterior over neural network weights, enabling model comparison via the Bayesian evidence — the simplest deterministic approach to Bayesian neural networks.
• Laplace Redux — Effortless Bayesian Deep Learning - factored and last-layer approximations; shows it is competitive with MC Dropout and ensembles (see Bayesian Deep Learning below) at a fraction of the cost, and provides the `laplace-torch` library.
• Score-based diffusion models for diffuse optical tomography with uncertainty quantification - Lam Duong* — Applies the diffusion posterior sampling framework to medical imaging, introducing a regularization strategy that blends learned and model-based scores to prevent overfitting; demonstrates calibrated uncertainty estimates with lower variance than classical Bayesian methods.
• Weight Uncertainty in Neural Networks
• Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning
• Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles - Bayesian alternative for uncertainty; despite its simplicity, deep ensembles empirically match or outperform both MC Dropout and Bayes by Backprop on calibration and out-of-distribution detection.
• Bayesian Deep Learning and a Probabilistic Perspective of Generalization - basin marginalization, and shows that Bayesian averaging resolves pathologies like double descent.
• Bayesian Computation in Deep Learning - MCMC (see above) and VI, covering their challenges (multimodality, cold posteriors) and solutions specific to deep neural networks and deep generative models.