efficient gibbs sampling

This work addresses the slow MCMC convergence in Gibbs posterior sampling under stochastic loss functions, which stems from spurious dependence on the number of pseudo-observations. We propose the first pseudo-sample-size–independent corrected piecewise deterministic Markov process (PDMP) sampler. By designing a novel jump-rate function and direction mechanism, our method rigorously ensures that the invariant measure remains invariant to the pseudo-observation count—thereby overcoming the inherent trade-off between asymptotic bias and slow convergence in conventional stochastic-loss inference. We prove that the sampler converges exactly to the target Gibbs posterior measure with a uniform convergence rate independent of pseudo-sample size. Empirical validation across three canonical settings—likelihood-intractable models, misspecified models, and stochastic losses—demonstrates elimination of pseudo-sample-size bias in posterior sampling, alongside substantial improvements in robustness and estimation accuracy.

In high-dimensional Bayesian sparse regression, Gibbs samplers suffer from poor efficiency due to slow mixing of the global scale parameter τ. This work proposes a novel approach that marginalizes out the regression coefficients when updating τ, enabling direct and efficient sampling from the collapsed posterior of τ by leveraging spectral decomposition and adaptive numerical integration—without requiring Metropolis–Hastings steps. The method achieves, for the first time, tuning-free direct sampling of τ under global–local shrinkage priors such as the horseshoe, substantially improving mixing efficiency and convergence speed. Its effectiveness and scalability are demonstrated on logistic regression tasks with dimensions as large as 120,000 × 1,379 and 1,980 × 17,848.

Traditional Gibbs sampling for Bayesian inference in finite mixture models suffers from low efficiency—particularly in high-dimensional electronic health record (EHR) clustering—due to redundant updates and slow convergence. To address this, we propose a discomfort-guided adaptive Gibbs sampling method, where “discomfort” quantifies the uncertainty of an observation’s current cluster assignment, enabling selective resampling only for low-confidence data points. This work is the first to integrate classification confidence modeling directly into the MCMC framework, dynamically adapting the update strategy via historical sampling trajectories. Experiments on both synthetic and real-world EHR datasets demonstrate that our method significantly accelerates posterior convergence (average speedup of 2.3×) and substantially reduces wasteful computation, outperforming state-of-the-art sampling techniques.

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 proposes an efficient posterior sampling method for ill-posed Bayesian inverse problems under linear observations by leveraging a diffusion model as a prior. The approach embeds a diffusion generative model within a Bayesian framework and introduces, for the first time, a tailored Gibbs sampling algorithm that ensures convergence of the Markov chain under certain conditions. By integrating the expressive power of diffusion priors, Bayesian regularization, and Gibbs-based MCMC, the method achieves a simple yet computationally efficient structure. Numerical experiments demonstrate that the proposed algorithm significantly outperforms existing strategies in terms of accuracy, stability, and computational efficiency in posterior sampling.

This work addresses the challenge of sampling from low-temperature Gibbs distributions whose support is constrained and whose modes may lie on the boundary of the domain—regions where the Laplace approximation breaks down. In this pre-asymptotic regime, the authors uncover a local product structure: the target distribution can be decomposed as a perturbed product of a strongly log-concave distribution over the regular interior and a one-dimensional exponential-family distribution capturing the non-regular boundary behavior. Leveraging this insight, they develop an efficient sampling algorithm that integrates Langevin dynamics and, for the first time, provide non-asymptotic sampling error guarantees for models with boundary modes. The method demonstrates both theoretical rigor and practical efficiency across several Bayesian inference tasks, including high-dimensional logistic regression, Poisson linear models, and Gaussian mixture models.

This work proposes the Automatic Slice Gibbs (ASG) framework to address the challenge of efficiently sampling from non-standardized, non-smooth, heavy-tailed, and highly multimodal distributions. ASG combines a Cauchy transformation to adaptively estimate the effective support set and employs slice-driven Gibbs updates to enable fully automatic Markov chain Monte Carlo (MCMC) sampling—requiring no user-specified truncation bounds, proposal scales, geometric priors, or gradient information. The method automatically handles disconnected high-density regions and complex geometric structures. Empirical evaluations on Beta mixtures, Rosenbrock, Ackley, and non-smooth LASSO-type posteriors demonstrate that ASG consistently achieves substantially higher effective sample sizes per unit time and faster decorrelation compared to random-walk Metropolis–Hastings, adaptive Gibbs samplers, and other slice sampling approaches.

This work addresses the challenges of multi-object posterior inference under non-standard observations, where conventional filtering approaches suffer from poor smoothness and loss of historical information. To overcome these limitations, the paper proposes a multi-scan multi-object smoothing algorithm based on Gibbs sampling. By constructing conditionally conjugate Bernoulli random field distributions that admit efficient computation and sampling, the method achieves, for the first time, Bayesian multi-object smoothing suitable for superpositional measurements, thereby breaking through the inference bottleneck imposed by non-standard sensing modalities. The approach jointly models object existence probabilities and attribute densities, significantly outperforming existing detection-based smoothing techniques in low signal-to-noise ratio scenarios while providing a complete statistical characterization of key variables and parameters.