Approximate Bayesian Inference

Approximate Bayesian inference tackles the challenge of estimating probability distributions over model parameters when direct calculation is intractable, aiming for efficient and accurate uncertainty quantification. Current research emphasizes developing scalable algorithms like variational inference and stochastic gradient MCMC, often coupled with neural networks (including Bayesian neural networks and large language models) to handle complex models and large datasets. These advancements are improving the reliability and robustness of machine learning models across diverse fields, from physics-informed modeling and large language model adaptation to reinforcement learning and economic agent-based modeling, by providing more accurate uncertainty estimates and better generalization. Furthermore, research is actively addressing limitations such as model misspecification and the computational cost of existing methods.