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:2504. 01894v2 Announce Type: replace Abstract: We present a bifidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution.
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:2606. 31284v1 Announce Type: new Abstract: Quantile regression aims to estimate the conditional quantiles of a response variable from observed data.
arXiv:2606. 27286v1 Announce Type: new Abstract: Mechanistic epidemiological models are widely used to support infectious disease forecasting and public-health decision making.
arXiv:2610.19074v1 Announce Type: new Abstract: Reliable uncertainty quantification remains an important challenge in AI. Hierarchical Bayesian methods provide a principled framework for this by repr...
arXiv:2406.17699v3 Announce Type: replace-cross Abstract: Assume that we would like to estimate the expected value of a function $F$ with respect to an intractable density $\pi$, which is specified u...
arXiv:2610.10194v1 Announce Type: cross Abstract: Switching stochastic differential equations (SSDEs) describe continuous-time dynamics whose parameters switch according to a latent regime process th...
Product Monte Carlo (PMC) is an algorithm that estimates expectations under a product of densities using only Monte Carlo samples from each individual density. By reformulating the intractable product expectation as a regression problem involving computable conditional expectations, PMC provides both point estimates and coherent Bayesian uncertainty quantification. The method achieves higher accuracy, better-calibrated uncertainty, and improved scalability compared to existing techniques, and it does not require density evaluations, enabling its use in simulation‑based inference such as protein image analysis.
Conditional Mean Flows introduce a new approach for simulation-based inference that replaces the costly numerical integration of traditional flow matching with few-step sampling and tractable density evaluation. By identifying conditional flow maps through a mean flow objective and using independent masking, the method allows direct estimation of marginal likelihoods. Experiments demonstrate that single-step conditional mean flow density evaluation achieves error comparable to 200-step flow matching while accelerating downstream MCMC sampling by roughly 200‑fold.
arXiv:2607. 21843v1 Announce Type: cross Abstract: Empirical Bayes (EB) performs simultaneous inference across many related latent variables.
arXiv:2410. 14843v4 Announce Type: replace-cross Abstract: Vanilla variational inference finds an optimal approximation to the Bayesian posterior distribution, but even the exact Bayesian posterior is often not meaningful under model misspecification.
arXiv:2609.39712v1 Announce Type: cross Abstract: We consider simulation-based Bayesian inference (SBI) for the parameters of models with intractable likelihoods but tractable forward simulation. Bui...