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.
By Maren Mahsereci, Toni Karvonen
arXiv:2606.15871v2 Announce Type: replace-cross
Abstract: Uncertainty in the solution of an inverse problem and in the tasks performed on it is quantified by posterior expectations, each an average o...
By Ali Siahkoohi
arXiv:2609. 27930v1 Announce Type: cross Abstract: We propose a Bayesian nonparametric mixture of regression trees with a Dirichlet process prior over tree-parameter pairs, enabling data-driven selection of ensemble size and unifying CART, BART, random forests, and boosting.
By Subhasish Basak, Anik Roy, Sourabh Bhattacharya
The paper presents an exact, efficient solution for the Linear Model of Co‑regionalization (LMC) multitask Gaussian Process by decoupling latent processes under a mild noise‑model assumption. It introduces a full parametrization of the resulting projected LMC, enabling linear‑time optimization and simplifying tasks such as training updates and leave‑one‑out cross‑validation. Experiments on synthetic and real data demonstrate that projected LMC is competitive with state‑of‑the‑art multitask GP models while offering greater interpretability and computational ease.
By Olivier Truffinet (CEA Saclay), Karim Ammar (CEA Saclay), Jean-Philippe Argaud (EDF R&D), Bertrand Bouriquet (EDF)
The paper introduces SME-BETEL, a semiparametric Bayesian method that merges score matching estimating equations with Bayesian exponentially tilted empirical likelihood to perform inference on models with intractable normalizing constants. SME-BETEL avoids evaluating these constants and eliminates the need for learning-rate calibration, while providing consistency, asymptotic normality, and a Bernstein‑von Mises theorem that guarantees asymptotically calibrated credible sets even under model misspecification. The authors extend the framework to mixed‑domain data, enabling robust inference for doubly‑intractable models such as spatial preferential sampling, and demonstrate its effectiveness through simulations and an ozone‑monitoring application.
By Jiongran Wang, Debdeep Pati, Anirban Bhattacharya
arXiv:2606. 27269v1 Announce Type: cross Abstract: Reliably quantifying predictive uncertainty is difficult for complex, high-dimensional, or misspecified models.
By Graham Gibson, John Tipton, Kellin Rumsey, Natalie Klein