arXiv:2606. 15871v1 Announce Type: cross Abstract: Bayesian inference for inverse problems is run to evaluate integrals -- posterior expectations, tail probabilities, and risks -- across a stream of observations.
arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.
arXiv:2602. 00387v4 Announce Type: replace-cross Abstract: Bayesian neural networks promise calibrated uncertainty but require $O(mn)$ parameters for standard mean-field Gaussian posteriors.
arXiv:2402. 11736v3 Announce Type: replace Abstract: Kernel herding belongs to a family of deterministic quadratures that seek to minimize the maximum mean discrepancy (MMD), that is, the worst-case integration error over a reproducing kernel Hilbert space (RKHS).
This survey article reviews Bayesian quadrature, a probabilistic, model‑based method for numerical integration and expectation estimation. It provides a systematic taxonomy of Bayesian quadrature techniques across modelling, inference, and sampling, presents theoretical guarantees, and includes a controlled numerical study illustrating the impact of different methodological choices. The paper also discusses practical challenges, limitations, and offers an extensive bibliography covering machine learning, statistics, mathematics, and engineering applications.
arXiv:2601. 07094v2 Announce Type: replace-cross Abstract: Bayesian optimization (BO) iteratively fits a Gaussian process (GP) surrogate to accumulated evaluations and selects new queries via an acquisition function.
The paper presents a non‑asymptotic analysis of Markov chain Monte Carlo (MCMC) algorithms that learn and apply a preconditioner based on either the target covariance or the expected Hessian of the target potential. It compares the finite‑time computational costs of these preconditioned schemes with unpreconditioned counterparts, providing guarantees for algorithms such as the Unadjusted Langevin Algorithm (ULA) and the proximal sampler. The analysis relies on a contraction assumption in the Wasserstein‑2 distance to formalize approximate independence and bridge modern MCMC theory with classical effective sample size heuristics.
arXiv:2610.01269v1 Announce Type: cross Abstract: Bayesian Optimisation (BO) is a powerful framework for the optimisation of expensive black-box functions, but typically requires refitting a surrogat...
arXiv:2603. 00393v2 Announce Type: replace-cross Abstract: Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy, incomplete data or inherent non-uniqueness.
arXiv:2607. 10793v1 Announce Type: new Abstract: Numerical integration is a cornerstone of various scientific computing applications, such as engineering simulations and model evidence computations in probabilistic machine learning.
The paper introduces a new approach to source distribution estimation (SDE) in simulation-based science, addressing limitations of existing methods that rely on a fixed surrogate likelihood. By employing an expectation‑maximization framework, the authors iteratively train an amortized posterior on fresh simulations (E‑step) and refit the source distribution to the posterior’s average (M‑step). Two parameterizations are explored: separate source and posterior flows, and a single shared conditional flow, with experiments on three benchmark tasks showing improved performance over fixed surrogate and iterated baseline methods, notably achieving higher data‑space C2ST scores on the Lotka–Volterra benchmark.
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.