mcmc

该论文提出了多层粒子边缘Metropolis-Hastings（MLPMMH）方法，通过伪边缘推断与跨网络宽度截断层级的耦合SMC相结合，实现分层贝叶斯深度学习中参数与超参数的联合推断，并在理论上证明了O(ε²)的均方误差与O(ε⁻²)的计算复杂度，同时给出可扩展的近似版本S-MLPMMH用于MNIST实验。

Kirk Borne 分享并推荐了教材《Bayes Rules!: An Introduction to Applied Bayesian Modeling》，该书由 Alicia A. Johnson、Miles Q. Ott 和 Mine Dogucu 编写，涵盖共轭先验、MCMC、回归与层级模型，并配有 bayesrule R 包。

本文提出 OSIS（one-step implicit sampler），利用短时间 MCMC 动力学为隐式建模分布定义局部目标，实现单步摊销采样。作者分析了收敛性质，并表明该方法在采样效率上优于多步摊销采样器和非摊销 MCMC 基线。

The author shares notes explaining Hamiltonian Monte Carlo (HMC) from a probabilistic perspective to enhance understanding without relying on physics-based motivation.

FLARE MCMC is a novel multi-fidelity method that enhances Markov chain Monte Carlo sampling by using layer-adaptive recursive proposals with lower-fidelity likelihood approximations, demonstrating improved efficiency in applications such as hydrology and cosmology.

This paper introduces a Bayesian approach to conditional causal discovery, where the posterior over causal graphs and parameters is conditioned on user-specified causal-effect constraints (e.g., a large causal effect). They adapt rare-event estimation techniques to handle events with small posterior mass and validate the method on synthetic data and the Sachs protein dataset.

This paper proposes a test-time alignment approach for large vision-language models using trajectory-guided structured sampling and iterative MCMC refinement, improving visual reasoning accuracy without heavy post-training.

This paper presents BayesPO, a Bayesian prompt optimization framework using gradient-guided discrete MCMC with parallel tempering, achieving improved accuracy on instruction-induction tasks.

Introduces Depth-Entropy Guided Sampling (DEGS), a training-free test-time method that exploits layer-wise entropy collapse in LLMs to improve reasoning without RL training, achieving competitive results with RL-posttrained models.

This paper introduces Entropy-Guided Power Sampling (EGPS), a training-free and verifier-free sampler that improves the efficiency of power sampling for enhancing base language model reasoning. EGPS achieves up to 12.6x speedup over standard Metropolis-Hastings sampling while reaching best or tied-best accuracy on benchmarks like MATH500, HumanEval, and GPQA.

This paper proposes a four-phase method for constructing causal graphs that model LLM inference processes, using counterfactual augmentation to enable stable causal discovery and provide transparent, concept-level explainability.

bde is a Python package that brings sampling-based Bayesian Deep Learning to practitioners via the MILE method, combining JAX's speed with scikit-learn's API for tabular supervised learning tasks.