The article compares three sampling methods—NumPyro’s NUTS, the affine‑invariant MCMC sampler Emcee, and the nested sampling algorithm dynesty—by benchmarking them against an exact ground truth. It evaluates how each sampler performs and documents their failures in practice. The comparison provides insights into the strengths and limitations of each approach for posterior inference.
arXiv:2606. 09926v1 Announce Type: cross Abstract: Sampling from the sequence-level power distribution $p^\alpha$ elicits RL-level reasoning from base language models without any parameter updates, but the standard Metropolis--Hastings (MH), a Markov Chain Monte Carlo (MCMC) sampler, is both expensive and slow-mixing.
The paper introduces duet sampling, a generalization of the Metropolis-Hastings algorithm that selects two proposal distributions from a pool at each iteration to resample parents for multiple nodes in a directed acyclic graph (DAG). This approach enables Markov chain moves that mix more efficiently without extra computational cost, outperforming existing state‑of‑the‑art methods in experiments. The authors demonstrate that their novel moves, both alone and combined, achieve superior performance even when previous methods also adopt duet sampling.
The paper introduces OSIS, a one‑step implicit sampler that uses short‑time MCMC dynamics to define a local target for an implicitly modelled distribution. In the asymptotic limit, the model converges to a fixed point of the MCMC kernel, enabling unbiased sampling from the Bayesian posterior. Experiments show OSIS outperforms multi‑step amortised samplers and non‑amortised MCMC baselines while being far more efficient at sampling time.
arXiv:2610.01448v1 Announce Type: cross Abstract: Skew-symmetric probability distributions provide a principled mechanism for incorporating gradient information into Markov chain Monte Carlo algorith...
arXiv:2507. 21449v2 Announce Type: replace-cross Abstract: Degeneracy is an inherent feature of the loss landscape of neural networks, but it is not well understood how stochastic gradient MCMC (SGMCMC) algorithms interact with this degeneracy.
arXiv:2610.20020v1 Announce Type: cross Abstract: It is folklore that passing "convergence" diagnostics does not guarantee that a Markov chain has converged. We prove this as an impossibility for any...
A fundamental challenge in Bayesian network structure learning lies in efficiently approximating the posterior distribution of directed acyclic graphs (DAGs). For large, high-dimensional datasets, the...
The paper introduces a two-step Metropolis–Hastings algorithm designed to efficiently sample from Bayesian empirical likelihood (BayesEL) posterior distributions, addressing challenges posed by the complex, often non‑convex support of empirical likelihood. The method leverages current parameter values and estimating equations to propose new values for remaining parameters, making it suitable for problems with discontinuous estimating equations such as simultaneous quantile regression. Additionally, the approach extends naturally to BayesEL model selection via reversible‑jump MCMC, and the authors demonstrate its utility through several real‑life applications.
arXiv:2506. 13058v2 Announce Type: replace-cross Abstract: Diffusion probabilistic models (DPMs) have demonstrated remarkable success in visual generation.
arXiv:2608. 13774v1 Announce Type: new Abstract: Markov chain Monte Carlo (MCMC) requires only the ability to evaluate the likelihood, making it a common technique for inference in complex models.
The paper "Nested Sampling: A Critical and Comprehensive Theoretical Guide" offers an in‑depth derivation of the nested sampling (NS) technique, clarifying its theoretical foundations and practical challenges. It explains how NS efficiently explores high‑likelihood regions, discusses its connections to importance sampling and vertical Monte Carlo, and highlights both strengths and limitations. The work serves as both a tutorial for newcomers and a critical review for experienced practitioners, aiming to inspire future enhancements and more efficient implementations across scientific fields.
The paper presents a continually learning neural‑operator surrogate for the three‑dimensional forward operator used in time‑domain airborne electromagnetic (AEM) Bayesian inversion. By training on successive geological priors and employing an ensemble‑disagreement validity check, the surrogate replaces the expensive forward solver, enabling the Markov chain Monte Carlo sampler to reproduce the full‑solver posterior with credible intervals within 2.6 % of the truth. Applied to the 2013 Capricorn TEMPEST survey, the surrogate inverts over two million soundings in seconds, making uncertainty‑quantified conductivity imaging at survey scale feasible for near real‑time mineral‑systems targeting.