Papers

Work in Progress

• Shen Z, Duran-Martin G, Oates CJ. Predictively-Oriented Kalman Filtering. arXiv
• Oates CJ, Howey R, Karvonen T. Sparse Probabilistic Richardson Extrapolation. arXiv
• Liu Q, Fisher MA, Shen Z, Zhao X, Tant K, Curtis A, Oates CJ. Detecting Model Misspecification in Bayesian Inverse Problems via Variational Gradient Descent. arXiv
• Chazal C, Kanagawa H, Shen Z, Korba A, Oates CJ. A Computable Measure of Suboptimality for Entropy-Regularised Variational Objectives. arXiv
• Xi M, Shen Z, Riabiz M, Chopin N, Oates CJ. Extrapolation of Tempered Posteriors. arXiv
• Shen Z, Wang H, Riabiz M, Oates CJ. Operator-Informed Score Matching for Markov Diffusion Models. arXiv

2026

• Fast Approximate Solutions of Stein Equations for Post-Processing of MCMC — Liu Q, Kanagawa H, Fisher MA, Briol F-X, Oates CJ. (2026) In: Lemieux C, Feng B (eds.). Monte Carlo and Quasi-Monte Carlo Methods 2024. Springer Verlag. Book arXiv
• Integrating imaging and invasive pressure data into a multi-scale whole-heart model — Strocchi M, Augustin CM, Gsell MA, Rinaldi CA, Vigmond EJ, Plank G, Oates CJ, Wilkinson RD, Niederer SA. (2026) Journal of Biomechanical Engineering, 148(5): 051001. Journal
• Harnessing the Power of Reinforcement Learning for Adaptive MCMC — Wang C, Fisher MA, Kanagawa H, Chen W, Oates CJ. AISTATS 2026. arXiv
• Stationary MMD Points for Cubature — Chen Z, Karvonen T, Kanagawa H, Briol FX, Oates CJ. ICML 2026. arXiv
• Thinned Mean Field Langevin Dynamics — Chen Z, Kanagawa H, Briol F-X, Oates CJ, Mackey L. ICML 2026. arXiv
• Calibrating Black-Box Probabilistic Numerical Methods — Chen J, Rau M, Oates CJ. Proceedings of the Second International Conference on Probabilistic Numerics, 2026.
• Extrapolating from Regularised Solutions for Solving Ill-Conditioned Linear Systems in Machine Learning — Hegde D, Cockayne J, Oates CJ. (2026) TMLR. Journal arXiv

2025

• GaussED: A Python Package for Sequential Experimental Design — Fisher MA, Teymur O, Oates CJ. Proceedings of the First International Conference on Probabilistic Numerics, 2025. arXiv
• Online Semiparametric Regression via Sequential Monte Carlo — Menictas M, Oates CJ, Wand MP. Australian & New Zealand Journal of Statistics, 67(2):224-249. Journal arXiv
• Probabilistic Richardson Extrapolation — Oates CJ, Karvonen T, Teckentrup AL, Strocchi M, Niederer SA. Journal of the Royal Statistical Society, Series B, 87(2):457-479. Journal arXiv
• Prediction-Centric Uncertainty Quantification via MMD — Shen Z, Knoblauch J, Power S, Oates CJ. Artificial Intelligence and Statistics (AISTATS 2025). video arXiv
• Reinforcement Learning for Adaptive MCMC — Wang C, Chen W, Kanagawa H, Oates CJ. Artificial Intelligence and Statistics (AISTATS 2025). arXiv

2024

• Minimum Kernel Discrepancy Estimators — Oates CJ. In: Hinrichs A, Kritzer P, Pillichshammer F (eds.). Monte Carlo and Quasi-Monte Carlo Methods 2022. Springer Verlag. Book arXiv
• The Matérn Model: A Journey through Statistics, Numerical Analysis and Machine Learning — Porcu E, Bevilacqua M, Schaback R, Oates CJ. Statistical Science, 39(3):469-492. Journal arXiv
• Grand Challenges in Bayesian Computation — Bhattacharya A, Linero A, Oates CJ (2024) ISBA Bulletin 31(3). arXiv

2023

• Gradient-Free Kernel Stein Discrepancy — Fisher M, Oates CJ. Advances in Neural Information Processing Systems (NeurIPS 2023). arXiv
• Stein Π-Importance Sampling — Wang C, Chen WY, Kanagawa H, Oates CJ. Advances in Neural Information Processing Systems (NeurIPS 2023). Selected for spotlight presentation. arXiv
• Stein's Method Meets Statistics: A Review of Some Recent Developments — Anastasiou A, Barp A, Briol F-X, Ebner B, Gaunt RE, Ghaderinezhad F, Gorham J, Gretton A, Ley C, Liu Q, Mackey L, Oates CJ, Reinert G, Swan Y. Statistical Science, 38(1): 120-139. Journal arXiv
• Regularised Zero-Variance Control Variates for High-Dimensional Variance Reduction — South LF, Oates CJ, Mira M, Drovandi C. Bayesian Analysis, 18(3): 865-888. Journal arXiv
• Maximum Likelihood Estimation in Gaussian Process Regression is Ill-Posed — Karvonen T, Oates CJ (2023) Journal of Machine Learning Research, 24(120):1-47. Journal arXiv
• Sobolev Spaces, Kernels and Discrepancies over Hyperspheres — Hubbert S, Porcu E, Oates CJ, Girolami M (2023) Transactions on Machine Learning Research. OpenReview arXiv
• Meta-learning Control Variates: Variance Reduction with Limited Data — Sun Z, Oates CJ, Briol FX. Conference on Uncertainty in Artificial Intelligence (UAI 2023). Selected for oral presentation. arXiv
• Cell to Whole Organ Global Sensitivity Analysis on a Four-chamber Electromechanics Model Using Gaussian Processes Emulators — Strocchi M, Longobardi S, Augustin CM, Gsell MAF, Petras A, Rinaldi CA, Vigmond EJ, Plank G, Oates CJ, Wilkinson RD, Niederer SA. PLoS Computational Biology, 19(6): e1011257. Journal
• Generalised Bayesian Inference for Discrete Intractable Likelihood — Matsubara T, Knoblauch J, Briol FX, Oates CJ. (2023) Journal of the American Statistical Society, 119(547), 2345-2355. Journal arXiv
• Statistical Properties of the Probabilistic Numeric Linear Solver BayesCG — Reid TW, Ipsen ICF, Cockayne J, Oates CJ. Numerische Mathematik, 155, 239-288. Journal arXiv
• Review of "Probabilistic Numerics" by Hennig, Osborne and Kersting — Oates CJ. SIAM Review, 65(3):905-915. Journal

2022

• Robust Generalised Bayesian Inference for Intractable Likelihoods — Matsubara T, Knoblauch J, Briol FX, Oates CJ. Journal of the Royal Statistical Society (Series B), 84(3):997-1022. Journal arXiv Video
• Optimal Thinning of MCMC Output — Riabiz M, Chen WY, Cockayne J, Swietach P, Niederer SA, Mackey L, Oates CJ. Journal of the Royal Statistical Society (Series B), 84(4):1059-1081. Journal arXiv Software
• Semi-Exact Control Functionals From Sard's Method — South LF, Karvonen T, Nemeth C, Girolami M, Oates CJ. Biometrika, 109(2):351-367. arXiv Software
• Scalable Control Variates for Monte Carlo Methods via Stochastic Optimization — Si S, Oates CJ, Duncan AB, Carin L, Briol F-X. Proceedings of the 14th International Conference in Monte Carlo & Quasi-Monte Carlo Methods in Scientific Computing, Springer 2022. Book arXiv
• Post-Processing of MCMC — South LF, Riabiz M, Teymur O, Oates CJ. Annual Reviews of Statistics and its Application, 9:529-555. Journal arXiv
• A Statistical Approach to Surface Metrology for 3D-Printed Stainless Steel — Oates CJ, Kendall WS, Fleming L. Technometrics, 64(3):370-383. Journal arXiv
• A Riemann-Stein Kernel Method — Barp A, Oates CJ, Porcu E, Girolami M. Bernoulli, 28(4): 2181-2208. Journal arXiv
• Testing Whether a Learning Procedure is Calibrated — Cockayne J, Graham MM, Oates CJ, Sullivan TJ. (2022) Journal of Machine Learning Research, 23(203):1-36. Journal arXiv
• Parameter Space Reduction for Four-chamber Electromechanics Simulations Using Gaussian Processes Emulators — Strocchi M, Longobardi S, Augustin CM, Gsell MAF, Vigmond EJ, Plank G, Oates CJ, Wilkinson RD, Niederer SA. Proceedings of the 10th Vienna International Conference on Mathematical Modelling, 2022.
• BayesCG As An Uncertainty Aware Version of CG — Reid TW, Ipsen ICF, Cockayne J, Oates CJ. Technical Report, 2022. arXiv

2021

• A Data-Centric Approach to Generative Modelling for 3D-Printed Steel — Dodwell TJ, Fleming LR, Buchanan C, Kyvelou P, Detommaso G, Gosling PD, Scheichl R, Kendall WS, Gardner L, Girolami MA, Oates CJ. Proceedings of the Royal Society A, 477(2255). Journal
• Probabilistic Iterative Methods for Linear Systems — Cockayne J, Ipsen ICF, Oates CJ, Reid TW. Journal of Machine Learning Research, 22(232):1-34. Journal arXiv
• Bayesian Numerical Methods for Nonlinear Partial Differential Equations — Wang J, Cockayne J, Chkrebtii O, Sullivan TJ, Oates CJ. Statistics and Computing, 31(55). Journal arXiv
• The Ridgelet Prior: A Covariance Function Approach to Prior Specification for Bayesian Neural Networks — Matsubara T, Oates CJ, Briol F-X. Journal of Machine Learning Research, 22(157):1-57. Journal arXiv
• Integration in Reproducing Kernel Hilbert Spaces of Gaussian Kernels — Karvonen T, Oates CJ, Girolami M. Mathematics of Computation, 90(331):2209-2233. Journal arXiv
• Optimal Quantisation of Probability Measures Using Maximum Mean Discrepancy — Teymur O, Gorham J, Riabiz M, Oates CJ. International Conference on Artificial Intelligence and Statistics (AISTATS 2021). Journal arXiv
• Causal Graphical Models for Systems-Level Engineering Assessment — Stephenson V, Oates CJ, Finlayson A, Thomas C, Wilson K. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 7(2):04021011. Journal
• Improved Calibration of Numerical Integration Error in Sigma-Point Filters — Prüher J, Karvonen T, Oates CJ, Straka O, Särkkä S. IEEE Transactions on Automatic Control, 66(3):1286-1292. Journal arXiv
• Measure Transport with Kernel Stein Discrepancy — Fisher MA, Nolan T, Graham MM, Prangle D, Oates CJ. AISTATS 2021. Selected for oral presentation (top 3%). Journal arXiv Software
• Black Box Probabilistic Numerics — Teymur O, Foley CN, Breen PG, Karvonen T, Oates CJ. Advances in Neural Information Processing Systems (NeurIPS 2021). Journal arXiv

2020

• Maximum Likelihood Estimation and Uncertainty Quantification for Gaussian Process Approximation of Deterministic Functions — Karvonen T, Wynne G, Tronarp F, Oates CJ, Särkkä S. SIAM Journal of Uncertainty Quantification, 8(3):926-958. Journal arXiv
• A Locally Adaptive Bayesian Cubature Method — Fisher MA, Oates CJ, Powell C, Teckentrup A. AISTATS 2020. Journal arXiv
• Discussion of "Unbiased Markov Chain Monte Carlo with Couplings" — South LF, Nemeth C, Oates CJ. Journal of the Royal Statistical Society (Series B), 82(3):590-592. Journal arXiv
• Optimality Criteria for Probabilistic Numerical Methods — Oates CJ, Cockayne J, Prangle D, Sullivan TJ, Girolami M. In Multivariate Algorithms and Information-Based Complexity, De Gruyter. arXiv
• A Role for Symmetry in the Bayesian Solution of Differential Equations — Wang J, Cockayne J, Oates CJ. Bayesian Analysis, 15(4):1057-1085. Journal arXiv

2019

• Editorial: Special Edition on Probabilistic Numerics — Girolami M, Ipsen I, Oates CJ, Owen A, Sullivan T. Statistics and Computing, 29(6):1181-1183. Journal
• Causal Learning via Manifold Regularization — Hill SM, Oates CJ, Blythe D, Mukherjee S. Journal of Machine Learning Research, 20:1-32. Journal arXiv
• Stein Point Markov Chain Monte Carlo — Chen WY, Barp A, Briol FX, Gorham J, Girolami M, Mackey L, Oates CJ. ICML 2019. Journal arXiv Software
• A Modern Retrospective on Probabilistic Numerics — Oates CJ, Sullivan TJ. Statistics and Computing, 29(6):1335-1351. Journal arXiv
• Bayesian Probabilistic Numerical Methods — Cockayne J, Oates CJ, Sullivan T, Girolami M. SIAM Review, 61(4):756-789. Journal arXiv
• Symmetry Exploits for Bayesian Cubature Methods — Karvonen T, Särkkä S, Oates CJ. Statistics and Computing, 29:1231-1248. Journal arXiv Software
• A Bayesian Conjugate Gradient Method — Cockayne J, Oates CJ, Ipsen I, Girolami M. (with discussion and rejoinder) Bayesian Analysis, 14(3):937-1012. Journal arXiv Software
• Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment — Oates CJ, Cockayne J, Aykroyd RG, Girolami M. Journal of the American Statistical Association, 114(528):1518-1531. Journal arXiv
• Optimal Monte Carlo Integration on Closed Manifolds — Ehler M, Gräf M, Oates CJ. Statistics and Computing, 29(6):1203-1214. Journal arXiv
• Convergence Rates for a Class of Estimators Based on Stein's Method — Oates CJ, Cockayne J, Briol F-X, Girolami M. (2019) Bernoulli, 25(2):1141-1159. Journal arXiv
• Probabilistic Integration: A Role in Statistical Computation? (with discussion and rejoinder) — Briol F-X, Oates CJ, Girolami M, Osborne MA, Sejdinovic D. Statistical Science, 34(1):1-22. Journal arXiv
• Graphical Models in Molecular Systems Biology — Mukherjee S, Oates CJ. In Handbook of Graphical Models, CRC Press. Preprint

2018

• A Bayes-Sard Cubature Method — Karvonen T, Oates CJ, Särkkä S. NeurIPS 2018. Journal arXiv
• Stein Points — Chen WY, Mackey L, Gorham J, Briol FX, Oates CJ. ICML 2018, PMLR 80:844-853. Journal arXiv

2017

• Probabilistic Models for Integration Error in Assessment of Functional Cardiac Models — Oates CJ, Niederer S, Lee A, Briol F-X, Girolami M. NIPS 2017. Journal arXiv
• On the Sampling Problem for Kernel Quadrature — Briol FX, Oates CJ, Cockayne J, Chen WY, Girolami M. (2017) ICML 2017, PMLR 70:586-595. Journal arXiv
• Discussion of "A Bayesian information criterion for singular models" — Friel N, McKeone JP, Oates CJ, Pettitt AN. (2017) Journal of the Royal Statistical Society (Series B), 79(2):323-380. Journal arXiv
• Repair of Partly Misspecified Causal Diagrams — Oates CJ, Kasza J, Simpson JA, Forbes AB. (2017) Epidemiology, 28(4):548-552. Journal PubMed
• Control Functionals for Monte Carlo Integration — Oates CJ, Girolami M, Chopin N. (2017) Journal of the Royal Statistical Society, Series B, 79(3):695-718. Journal arXiv
• Investigation of the Widely Applicable Bayesian Information Criteria — Friel N, McKeone JP, Oates CJ, Pettitt AN. (2017) Statistics and Computing, 27(3):833-844. Journal arXiv

2016

• Probabilistic Numerical Methods for PDE-constrained Bayesian Inverse Problems — Cockayne J, Oates CJ, Sullivan T, Girolami M (2016) AIP Conference Proceedings, 1853:060001. Journal arXiv
• Discussion of "Causal inference using invariant prediction: identification and confidence intervals" — Oates CJ, Kasza J, Mukherjee S (2016) Journal of the Royal Statistical Society (Series B), 78(5):947-1012. Journal arXiv
• RNA editing generates sequence diversity within cell populations — Harjanto D, Papamarkou T, Oates CJ, Rayon Estrada V, Papavasiliou FN, Papavasiliou A. (2016) Nature Communications, 7:12145. Journal
• Control Functionals for Quasi-Monte Carlo Integration — Oates CJ, Girolami M. (2016) AISTATS, JMLR W&CP, 51:56-65. Selected for Oral Presentation (top 6.5% of submissions). Journal arXiv
• Estimation of Causal Structure Using Conditional DAG Models — Oates CJ, Smith JQ, Mukherjee S. (2016) Journal of Machine Learning Research, 17(54):1-23. Journal arXiv
• The Controlled Thermodynamic Integral for Bayesian Model Evidence Evaluation — Oates CJ, Papamarkou T, Girolami M (2016) Journal of the American Statistical Association, 111(514):634-645. Journal arXiv
• Exploiting Multi-Core Architectures for Reduced-Variance Estimation with Intractable Likelihoods — Friel N, Mira A, Oates CJ (2015) Bayesian Analysis, 11(1):215-245. Journal arXiv
• Exact Estimation of Multiple Directed Acyclic Graphs — Oates CJ, Smith JQ, Mukherjee S, Cussens J (2016) Statistics and Computing, 26(4):797-811. Journal arXiv

2015

• Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees — Briol F-X, Oates CJ, Girolami M, Osborne MA. (2015) NIPS 2015. Selected for Spotlight Presentation. Journal arXiv
• Decoupling of the PI3K pathway via mutation necessitates combinatorial treatment in HER2+ breast cancer — Korkola JE, Collisson EA, Heiser L, Oates CJ, et al. (2015) PLoS One, 10(7):e0133219. Journal
• Accelerated Nonparametrics for Cascades of Poisson Processes — Oates CJ. (2015) Stat, 4(1):183-195. Journal arXiv
• Discussion of "Sequential Quasi-Monte Carlo" by Gerber and Chopin — Oates CJ, Simpson D, Girolami M (2015) Journal of the Royal Statistical Society (Series B), 77(3):555-556. Journal arXiv
• Towards a Multi-Subject Analysis of Neural Connectivity — Oates CJ, Costa L, Nichols T (2015) Neural Computation, 27:151-170. Journal arXiv

2014

• Quantifying the Multi-Scale Performance of Network Inference Algorithms — Oates CJ, Amos R, Spencer SEF (2014) Statistical Applications in Genetics and Molecular Biology 13(5):611-631. Journal arXiv
• Joint Estimation of Multiple Related Biological Networks — Oates CJ, Korkola J, Gray JW, Mukherjee S (2014) The Annals of Applied Statistics 8(3):1892-1919. Journal arXiv
• Causal network inference using biochemical kinetics — Oates CJ, Dondelinger F, Bayani N, Korkola J, Gray JW, Mukherjee S (2014) Bioinformatics 30(17):i468-i474. Best Paper at the European Conference on Computational Biology 2014. Journal arXiv
• Joint Structure Learning of Multiple Non-Exchangeable Networks — Oates CJ, Mukherjee S (2014) AISTATS, JMLR W&CP 33:687-695. Journal arXiv
• Single-Cell States in the Estrogen Response of Breast Cancer Cell Lines — Casale FP, et al. (2014) PLoS One 9(2):e88485. Journal
• A stochastic model dissects cellular states and heterogeneity in transition processes — Armond J, Saha K, Rana AA, Oates CJ, Jaenisch R, Nicodemi M, Mukherjee S (2014) Nature Scientific Reports 4:3692. Journal

2013

• Bayesian Inference for Protein Signalling Networks — Oates CJ (2013) PhD Thesis. pdf
• Self Organisation and Emergence — Chau Y-X, Oates CJ, Rana AA, Robinson L, Nicodemi M. (2013) In: Complexity Science: The Warwick Master's Course, Cambridge University Press.

2012

• Network Inference and Biological Dynamics — Oates CJ, Mukherjee S (2012) The Annals of Applied Statistics 6(3):1209-1235. Journal arXiv
• Network Inference Using Steady State Data and Goldbeter-Koshland Kinetics — Oates CJ, Hennessy BT, Lu Y, Mills GB, Mukherjee S (2012) Bioinformatics 28(18):2342-2348. Journal arXiv