run reversible-jump mcmc

This work addresses the challenge of posterior inference in chained Markov fusion models, where shared variables between adjacent submodels complicate computation. To overcome this, the authors propose a multi-stage sequential Monte Carlo (SMC) sampler based on a divide-and-conquer strategy. This approach introduces divide-and-conquer SMC into the chained Markov fusion framework for the first time, decomposing the model using a tree structure to enable flexible composition of an arbitrary number of heterogeneous submodels and efficient Bayesian inference. Experimental results demonstrate that the method accurately estimates key parameters—such as immigration and reproduction rates—in both a synthetic example comprising 11 submodels and an ecological integrated population model, significantly improving inference efficiency and scalability.

Diffusion models suffer from low sampling efficiency and high variance in posterior inference under highly informative likelihoods or anomalous observations. To address this, we propose a correlation-aware sequential Monte Carlo (SMC) sampler for diffusion posteriors. Our method introduces an observation-guided diffusion path tightly coupled with the forward process, enabling the proposal distribution to closely track the true posterior evolution. We further design path-dependent resampling and propagation mechanisms, substantially improving SMC’s statistical efficiency in challenging regimes. Experiments across multiple high-information-likelihood inverse problems demonstrate that our approach reduces sampling variance by 30–50% compared to standard diffusion SMC methods. Moreover, it exhibits markedly enhanced robustness under outlier conditions. By jointly modeling observational information and diffusion dynamics, our framework establishes a new paradigm for efficient and stable Bayesian inversion in difficult settings.

To address the high computational cost of slice sampling in Bayesian inference with expensive likelihood evaluations, this paper proposes a hybrid slice sampler incorporating the Delayed Acceptance (DA) mechanism. This work is the first to integrate DA into the slice sampling framework, leveraging a deterministic approximation of the target density to significantly reduce the number of expensive exact density evaluations per iteration—while preserving ergodicity. We provide theoretical guarantees establishing the ergodicity of the resulting Markov chain. Numerical experiments across multiple benchmarks demonstrate that, compared to standard slice sampling and DA-enabled Metropolis–Hastings, the proposed method achieves comparable sampling accuracy while reducing costly density evaluations by 60%–85%, thereby substantially improving computational efficiency. The core contribution lies in the principled integration of DA with slice sampling and the rigorous convergence analysis ensuring its validity.

Gibbs sampling for Bayesian mixture models suffers from slow mixing in the marginal posterior over component assignments and struggles to jointly perform model selection and parameter inference. Method: We propose two novel joint-sampling MCMC algorithms: (1) a collapsed Gibbs sampler incorporating unconventional move sets, and (2) a prior-driven, rejection-free component allocation sampler. Both methods jointly update observation assignments and the number of components, unifying model fitting and dimensionality inference. Contribution/Results: Our approaches eliminate the need for post-hoc model selection and substantially improve Markov chain mixing efficiency. In latent class analysis tasks, they reduce mixing time by several-fold compared to state-of-the-art methods while achieving comparable or superior posterior inference accuracy. The framework provides an efficient, fully automated computational solution for high-dimensional Bayesian nonparametric modeling.

This paper addresses the theoretical performance limits of lifted samplers in Markov chain Monte Carlo (MCMC), specifically analyzing the asymptotic variance relative to conventional reversible base algorithms such as Metropolis–Hastings (MH). Method: Building upon Tierney’s (1998) Markov chain convergence theory, the authors develop a unified framework integrating lifted dynamics modeling, abstraction of direction-inducing mechanisms, and spectral analysis of transition operators. Contribution/Results: The work establishes, for the first time, a universal upper bound: for any target distribution, any direction construction, and any reversible base algorithm (e.g., MH or reversible jump MCMC), the asymptotic variance of a lifted sampler is at most twice that of its base counterpart. This bound is independent of state-space ordering, the specific form of direction definition, or implementation details of the base algorithm—and incurs no additional computational overhead. The result provides a rigorous, general guarantee that lifting yields bounded improvement with controllable risk.

This work addresses the challenges of sampling from high-dimensional probability distributions, which are often hindered by the curse of dimensionality and metastable multimodal traps. It introduces a novel approach that repurposes generative models—such as normalizing flows and diffusion models—from their conventional data-driven paradigm into data-free auxiliary tools for efficient and accurate sampling from target distributions known only up to an unnormalized density. By integrating Monte Carlo methods with enhanced sampling techniques, the authors develop a tailored training strategy and systematically formulate a unified framework for generative-model-assisted sampling. This contribution offers a theoretically grounded and practically implementable tutorial, serving as both a methodological guide and a springboard for interdisciplinary research at the intersection of physics and machine learning.

This work addresses the slow convergence and strong dimension dependence of traditional MCMC methods in high- and infinite-dimensional Bayesian posterior sampling by proposing and analyzing two novel multi-proposal preconditioned Crank–Nicolson algorithms, termed mpCN and MTpCN. Leveraging parallelized proposal mechanisms, these algorithms achieve enhanced sampling efficiency and are shown to converge under non-convex, high-dimensional settings. The study establishes, for the first time, rigorous dimension-independent and proposal-number-uniform exponential convergence rates for both methods. By innovatively constructing two coupling schemes, the authors derive Wasserstein contraction, an $L^2$ spectral gap, and non-asymptotic statistical guarantees. The theory demonstrates that dimension-independent mixing is attainable without convexity assumptions, provided the log-likelihood is bounded and Lipschitz. Numerical experiments confirm faster warm-up and more robust parameter tuning, significantly outperforming standard pCN and independent parallel-chain approaches.

This work addresses the challenge of inefficient posterior exploration in hierarchical discrete models with latent variables, where conventional MCMC methods struggle due to the need to integrate out latent variables. The authors propose a similarity-driven MCMC approach that constructs a proposal mechanism based on a data-driven measure of discrepancy between observations and model predictions, thereby guiding transitions toward regions of higher posterior support without explicitly integrating latent variables. This method represents the first application of similarity-driven proposals to discrete-space MCMC and is naturally suited to complex hierarchical discrete models. Experiments on both synthetic and real-world data demonstrate substantial improvements in sampling efficiency and posterior exploration, confirming its effectiveness in models such as Dirichlet–Multinomial regression.

This study addresses the high variance inherent in Markov chain Monte Carlo (MCMC) sampling and the limitation of control variate methods that rely on analytical solutions to the Poisson equation, which restricts their applicability to general target distributions. To overcome these challenges, this work proposes a variance reduction framework based on normalizing flows. By leveraging bijective transformations to map the target distribution into a reference latent space, the authors derive the transformed Markov kernel and an explicit solution to the corresponding Poisson equation. This approach extends exact control variates to arbitrary target distributions and unifies the theoretical frameworks of importance sampling and control variates. Experimental results demonstrate that the proposed method significantly outperforms state-of-the-art samplers and existing control variate techniques on both synthetic and real-world posterior distributions.

Traditional MCMC methods suffer from low sampling efficiency in complex distributions, while multi-proposal MCMC (MP-MCMC) offers parallelization potential but lacks a clear theoretical understanding of its behavior and optimization mechanisms under a large number of proposals. This work establishes a general theoretical framework for multi-proposal involutive MCMC in abstract state spaces, systematically analyzing the properties of transition kernels under various proposal and acceptance schemes. It introduces three novel algorithms (Algs. 1.1, 3.3, 3.4), unifies existing MP-MCMC approaches by revealing their intrinsic connections, and eliminates ineffective strategies. Through asymptotic analysis in the large-proposal limit and a unified modeling perspective, the study clarifies convergence and efficiency properties under high parallelism, providing both theoretical foundations and practical algorithms for large-scale parallel MCMC.