sampling strategies

This paper addresses the optimal design of proposal densities in Monte Carlo importance sampling, particularly under challenging settings involving dynamic updates and noise—such as in Approximate Bayesian Computation (ABC) and policy evaluation in reinforcement learning. It provides the first unified theoretical analysis of the applicability boundaries of multiple optimality criteria—including minimum variance and KL-divergence minimization—while establishing a cross-framework evaluation framework that jointly ensures theoretical guarantees and empirically comparable performance. Methodologically, the work integrates variational inference, sequential importance resampling, and annealed posterior modeling to propose a multi-proposal adaptive mechanism. Key contributions are: (1) necessary and sufficient conditions for proposal optimality across frameworks, with convergence guarantees; (2) systematic empirical validation of trade-offs among model selection accuracy, noise robustness, and computational efficiency in adaptive proposal design; and (3) an open-source empirical benchmark enabling reproducible, standardized comparison of future proposal mechanisms.

Bayesian inference under computationally expensive and nonsmooth likelihoods remains challenging due to prohibitive evaluation costs and the absence of reliable gradients. Method: This paper proposes a subset-driven delayed-acceptance MCMC framework comprising: (1) a data-driven surrogate model evaluated on random subsets—eliminating reliance on inaccurate gradients or Taylor approximations; (2) a computation-aware adaptive controller that jointly tunes proposal scale and subset size; and (3) a hierarchical delayed-acceptance mechanism that rapidly filters candidates via the coarse surrogate and rigorously validates them on the full dataset. Results: On real-world high-cost inference tasks—including disease modeling—the method significantly reduces sampling error under fixed computational budgets, balancing exploration efficiency and posterior accuracy. It outperforms state-of-the-art baselines (e.g., standard DA-MCMC, HINTS) in both convergence speed and estimation accuracy.

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 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.

In Gibbs sampling, drawing from nonstandard univariate conditional distributions—lacking closed-form samplers and resisting efficient proposal construction for rejection sampling—remains challenging. Method: This paper proposes the Adaptive Vertical Weighted Strip (VWS) method, which constructs a finite mixture proposal distribution and dynamically optimizes component weights online to achieve low rejection rates with substantially reduced computational overhead. Contribution/Results: The key innovation lies in embedding VWS within the Gibbs framework, enabling iterative pruning of ineffective components and self-tuning of the proposal structure. Applied to small-area estimation, VWS enables efficient and accurate Bayesian inference for the posterior distribution of school-age children living in poverty at the county level. It thus enhances both the feasibility and practicality of Gibbs sampling for large-scale, complex hierarchical models.

To address the high variance and slow convergence of Markov chain Monte Carlo (MCMC) estimators for expectations, this paper proposes a general, unbiased control variate framework—the first systematic approach for automatic variance reduction applicable to arbitrary MCMC chains. Grounded in regeneration theory for Markov chains and the Riesz representation theorem, the method constructs control variates using polynomial or neural network basis functions, requiring neither gradient information nor model-specific assumptions. Adaptive weight optimization ensures efficient variance suppression. Evaluated on multiple Bayesian inference benchmarks, the method reduces estimator variance by 3–10×, substantially accelerating effective sample size accumulation while incurring negligible additional computational cost. The core contributions lie in the unification of four key properties: generality across MCMC kernels, statistical unbiasedness, gradient-free implementation, and adaptive weighting—enabling robust, plug-and-play variance reduction without compromising theoretical guarantees.

This work addresses the challenge of efficiently sampling from non-uniform density functions over linearly constrained domains in Bayesian inverse problems, particularly when conventional gradient-based methods degrade near domain boundaries. The authors propose a novel Markov chain Monte Carlo (MCMC) algorithm that uniquely integrates higher-order geometric information—specifically, both gradient and curvature—of the target density into a Hit-and-Run proposal mechanism. By doing so, the method rigorously preserves sample feasibility while substantially enhancing sampling efficiency. Empirical evaluations demonstrate that the proposed approach consistently outperforms existing constrained and unconstrained samplers across a range of complex linear constraint settings, exhibiting superior robustness and adaptability.

This study addresses the loss of sampling efficiency in stratified sampling under heteroscedastic populations, which arises when stratum variances are unknown and must be estimated. To tackle this issue, the authors propose a novel optimal sample allocation strategy grounded in Bayesian decision theory, specifically tailored for heteroscedastic univariate regression models. This approach extends Bayesian optimal experimental design to heteroscedastic settings for the first time, overcoming a key limitation of conventional Bayesian sampling designs that assume homoscedasticity and rely on suboptimal point estimates of design parameters. Empirical evaluations on both synthetic data and real-world IRS Form 990 charitable organization revenue data demonstrate that the proposed method consistently matches or outperforms established stratified sampling and model-assisted benchmark approaches.

This work addresses the challenges of inefficient sampling and excessive variance in Monte Carlo estimation arising from scale disparities among modes and low-density regions in multimodal distributions. To overcome these issues, the authors propose a modular Markov chain Monte Carlo (MCMC) method that constructs parallel Markov chains confined to subsets of the target space and combines their estimates via weights derived from inter-subset transition probabilities. By innovatively integrating parallel constrained sampling with a principled weighted fusion mechanism, the approach substantially enhances sampling efficiency and reduces estimator variance, yielding more robust multimodal expectation estimates within simulated annealing frameworks. Theoretical justification is provided through central limit theorem–type results, and numerical experiments—including Bayesian sparse regression with spike-and-slab priors—demonstrate the method’s superior performance.

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.