in-and-out sampling

This paper addresses the slow convergence of finite ergodic Markov chains by proposing an acceleration framework based on permutations and projections. Methodologically, it establishes—for the first time—the equivalence between the mixing time of permuted Markov chains and information-theoretic projections (measured via KL divergence or squared Frobenius norm); introduces an alternating projection algorithm that geometrically unifies the mixing process and reveals intrinsic connections to the Sylvester equation and assignment problem, yielding a trace-based criterion for stationarity. Theoretical contributions include: reducing the relaxation time from exponential to polynomial order for bimodal distributions; achieving logarithmic mixing time under random permutations—surpassing the linear bound of Diaconis–Holmes–Neal; and demonstrating significantly improved mixing efficiency over standard Metropolis–Hastings in physical model experiments.

This work addresses the challenge of verifying ergodicity for adaptive MCMC algorithms in non-compact state and parameter spaces, where traditional compactness assumptions fail. By abandoning such restrictive assumptions, the authors instead introduce probabilistic bounds on the sample and parameter sequences to formulate a new set of easily verifiable sufficient conditions. Integrating tools from MCMC theory, adaptive algorithm analysis, and concentration inequalities, they establish a novel ergodicity framework that operates without compactness requirements. This approach significantly enhances the practical applicability and tractability of convergence analysis in complex real-world settings where non-compactness is inherent.

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 challenge of simultaneously achieving non-reversibility, low discretization error, and computational efficiency in Piecewise Deterministic Markov Process (PDMP)-based MCMC methods. We propose a numerical approximation framework grounded in operator splitting, yielding both adaptive and non-adaptive samplers—marking the first systematic incorporation of splitting schemes into PDMP design (e.g., Bouncy Particle Sampler, Zig-Zag Sampler), augmented with a non-reversible Metropolis–Hastings correction to eliminate discretization bias. Each iteration requires only a single gradient evaluation while attaining second-order weak convergence. Theoretically, we establish geometric ergodicity criteria and derive an asymptotic expansion of the invariant measure with respect to step size. Experiments on Bayesian inverse problems in imaging and interacting particle systems demonstrate substantial gains in sampling efficiency over state-of-the-art baselines, confirming the method’s rigorous theoretical foundation and practical scalability.

This paper investigates the relationship between the convergence properties of ideal and hybrid slice sampling, specifically focusing on the mutual inheritance of convergence rates under the weak Poincaré inequality framework. Method: We develop a unified Dirichlet form comparison methodology, integrating Markov chain spectral theory with models of slice sampling variants—including stepping-out shrinkage and Hit-and-Run-within-Slice—and systematically apply the weak Poincaré inequality to analyze and compare their convergence behaviors. Contribution/Results: Under mild regularity assumptions, we establish that convergence rates of ideal and hybrid slice samplers are mutually derivable, providing a general theoretical guarantee for convergence transferability. Our framework extends to independent Metropolis–Hastings and multiple slice sampling variants, offering novel theoretical foundations for algorithm selection and design in high-dimensional Bayesian inference.

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.

研究解决了轻尾目标分布下Metropolis接受率不稳定的问题，通过无梯度随机游走Metropolis采样方法，在合理选择提议方差时保持了稳定的接受概率。

This work addresses the challenge of efficient sampling from unnormalized densities, circumventing the time discretization errors and score estimation biases inherent in conventional approaches. By embedding the target distribution as the initial marginal of a finite-time reverse diffusion process and leveraging an Ornstein–Uhlenbeck process to construct the Radon–Nikodym derivative, the authors establish a measure transformation framework that requires neither discretization nor score estimation. Building on this foundation, they propose two algorithms: a fully parallel, approximately i.i.d. sampler and a path-space Markov chain Monte Carlo (MCMC) update mechanism, where acceptance probabilities are realized via a Barker-type Bernoulli factory. The unified framework demonstrates substantial improvements over random-walk Metropolis on multimodal and strongly dependent distributions, offering both scalability and computational efficiency.

This work addresses the inefficiency and lack of a unified theoretical understanding of gradient-based MCMC methods when sampling from anisotropic and hierarchical posteriors. Starting from continuous-time dynamics, the authors systematically derive algorithms such as HMC, MALA, NUTS, and MAKLA through numerical discretization and Metropolis correction, establishing a cohesive theoretical framework. They introduce two key innovations: a globally whitened mass matrix and a stochastic step-size strategy, which together mitigate sampling difficulties arising from state-dependent curvature. The proposed approach substantially improves sampling efficiency and demonstrates superior convergence and stability in large-scale Bayesian inference and hierarchical models.

本文提出MarCo算法，通过从边缘分布进行Metropolis-Hastings采样并结合精确条件分布采样，解决了大尺度问题中MCMC算法计算成本高的问题，证明了其在混合时间和收敛性上的优越性能。