quotient posterior sampling

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.

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.

Bayesian posterior sampling on Riemannian manifolds—such as Stiefel and Grassmann manifolds—is challenging, especially under anisotropic target densities; existing gradient-based or preconditioning-dependent methods suffer from poor robustness. Method: We propose the first geodesic-based slice sampling MCMC algorithm for Riemannian manifolds, generalizing Euclidean hit-and-run slice sampling by replacing straight-line segments with geodesics. Our method is gradient-free, requires no pre-tuning, satisfies detailed balance, and is geometrically adaptive. Contribution/Results: We establish theoretical guarantees of ergodicity and detailed balance. Empirical evaluation on synthetic and real-world data demonstrates faster convergence and superior mixing compared to state-of-the-art manifold MCMC methods. Crucially, our algorithm remains stable and efficient even under highly anisotropic posteriors, significantly enhancing the practicality and robustness of Bayesian inference on matrix manifolds.

To address the challenge of sampling from high-dimensional, multimodal Bayesian posteriors, this paper proposes the Annealed Leap-Point Sampler (ALPS). Methodologically, ALPS introduces a novel “annealed” state-space augmentation: it constructs an annealed cold-state target distribution, locates modes via Laplace approximation, and enables efficient inter-modal transitions in the ultra-cold regime using Gaussian mixture–based independent Metropolis–Hastings. A temperature ladder then transfers this cross-modal capability to the original posterior. Theoretically, we prove that the coldest inverse temperature required scales only as *O*(*d*), and the overall algorithmic complexity is *O*(*d*³), markedly improving upon existing parallel tempering methods. Empirical evaluation on a high-dimensional multimodal SUR longitudinal model demonstrates ALPS’s robust inter-modal sampling performance, scalability to high dimensions, and guaranteed convergence.

Metropolis–Hastings samplers—especially informed variants—exhibit slow convergence and dimension-dependent relaxation times in high-dimensional discrete parameter spaces under multimodal posteriors. Method: We develop the first dimension-free mixing time theory for information-driven MCMC on discrete domains, integrating multicommodity flow analysis with single-site drift conditions and leveraging high-dimensional statistical structure to derive verifiable sufficient conditions. Contribution/Results: Our analysis yields a tight, dimension-independent upper bound on the relaxation time, breaking the conventional dimensional dependence bottleneck in convergence analysis. This provides the first theoretically grounded, computationally efficient sampling framework for discrete-parameter inference tasks—such as Bayesian model selection—where scalability with dimension is critical. The bound is constructive and applicable to a broad class of informed discrete MCMC algorithms, enabling rigorous performance guarantees without restrictive assumptions on posterior geometry or sparsity.

This study investigates the optimal scaling of high-dimensional Metropolised MCMC algorithms, focusing on how to adjust proposal distributions with increasing dimensionality to maintain sampling efficiency. Building upon the symmetry of the Metropolis–Hastings algorithm and high-dimensional asymptotic analysis, the authors develop a unified framework applicable to a broad class of target distributions and proposal mechanisms. The approach not only recovers classical results—such as the $O(1/d)$ variance scaling for Random Walk Metropolis (RWM) and $O(1/d^{1/3})$ for Metropolis-Adjusted Langevin Algorithm (MALA)—but also derives a novel class of gradient-driven MALA proposals with an optimal scaling law: their variance can be set to $O(1/d^\mu)$ for arbitrarily small $\mu > 0$, substantially outperforming existing methods. The theoretical analysis integrates non-product target measures and proposal distributions generated by implicit integrators of differential equations, demonstrating enhanced adaptability to dimensionality.

This study addresses the limitation of standard MCMC diagnostics, which frequently misinterpret multimodal posteriors as sampling failures. To overcome this, it proposes a graph-theoretic convergence diagnostic framework that constructs a graph structure by computing between-chain R-hat values, thereby identifying groups of Markov chains exploring the same posterior mode. The method is implemented using Stan and the R package mcmcConvergenceGraph. As the first approach to leverage graph structures for distinguishing genuine multimodality from poor mixing, it prevents the penalizing misdiagnosis of multimodal posteriors. By providing both graphical and numerical summaries, the framework offers comprehensive diagnostic insights. Its effectiveness in accurately diagnosing multimodal behavior is validated through applications in regression and pharmacokinetic models.

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.

This study addresses the challenge of parameter inference in ordinary differential equation models arising from structural non-identifiability. It introduces, for the first time, an explicit integration of structural identifiability analysis into the design of Markov chain Monte Carlo (MCMC) algorithms, proposing two novel sampling strategies: one constructs efficient proposals both within and orthogonal to the non-identifiable manifold, while the other performs inference in a low-dimensional space of identifiable parameter combinations and subsequently reconstructs the full parameter vector. By combining geometric MCMC with pseudo-marginal MCMC techniques, the method establishes a Bayesian inference framework tailored to equivalence solution manifolds. This approach significantly enhances sampling efficiency and convergence speed compared to standard MCMC methods, while preserving posterior correctness and chain ergodicity.

This study addresses the inefficiency of gradient utilization and inadequate adaptation to manifold geometry in Markov chain Monte Carlo (MCMC) sampling. Grounded in skew-symmetric distribution theory, this work proposes a coordinate-free Barker proposal algorithm along with its Gibbs and manifold variants. Methodologically, a Gibbs re-evaluation mechanism is introduced to enhance sampling efficiency for highly correlated targets, while a simplified manifold framework is constructed to improve robustness against irregular geometric structures. Experimental results demonstrate that the proposed Gibbs variant significantly improves sampling performance on correlated targets. Furthermore, when local geometric information is unreliable, the manifold-based Barker algorithm substantially outperforms the Metropolis-adjusted Langevin algorithm (MALA), offering a novel paradigm for efficient sampling in spaces with complex geometries.