Project Euclid

References

• Briol, F.-X., Oates, C. J., Girolami, M., Osborne, M. A., and Sejdinovic, D. (2015). “Probabilistic Integration: A Role for Statisticians in Numerical Analysis?” arXiv:1512.00933.
  arXiv: arXiv:1512.00933
  
• Cockayne, J., Oates, C. J., Sullivan, T., and Girolami, M. (2016). “Probabilistic Meshless Methods for Partial Differential Equations and Bayesian Inverse Problems.” arXiv:1605.07811.
  arXiv: arXiv:1605.07811
  
• Conrad, P., Girolami, M., Särkkä, S., Stuart, A., and Zygalakis, K. (2016). “Statistical Analysis of Differential Equations: Introducing Probability Measures on Numerical Solutions.” Statistics and Computing.
• Owhadi, H. (2015). “Bayesian Numerical Homogenization.” SIAM Multiscale Modeling & Simulation, 13(3): 818–828.
• Owhadi, H. and Scovel, C. (2015). “Conditioning Gaussian Measure on Hilbert Space.” arXiv:1506.04208.
  arXiv: arXiv:1506.04208
  
• Schober, M., Duvenaud, D., and Hennig, P. (2014). “Probabilistic ODE Solvers with Runge–Kutta Means.” In Advances in Neural Information Processing Systems, 739–747.
• Teymur, O., Zygalakis, K., and Calderhead, B. (2016). “Probabilistic Linear Multistep Methods.” In Advances in Neural Information Processing Systems. arXiv:1610.08417.
  arXiv: arXiv:1610.08417
  
• Chkrebtii, O. A., Campbell, D. A., Calderhead, B., and Girolami, M. A. (2016). “Bayesian solution uncertainty quantification for differential equations.” Bayesian Analysis, Advance publication.
• Schumaker, L. (2007). Spline Functions: Basic Theory. Cambridge University Press, New York, third edition.
• Yoo, W. W. and Ghosal, S. (2016). “Supremum norm posterior contraction and credible sets for nonparametric multivariate regression.” Annals of Statistics, 44(3): 1069–1102.
• Cockayne, J., Oates, C. J., Sullivan, T., and Girolami, M. (2016). “Probabilistic Meshless Methods for Partial Differential Equations and Bayesian Inverse Problems.” arXiv:1605.07811.
  arXiv: arXiv:1605.07811
  
• Kersting, H. and Hennig, P. (2016). “Active Uncertainty Calibration in Bayesian ODE Solvers.” In Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence (UAI 2016), 309–318. AUAI Press.
• Schober, M., Särkkä, S., and Hennig, P. (2016). “A Probabilistic Model for the Numerical Solution of Initial Value Problems.” arXiv:1610.05261.
  arXiv: arXiv:1610.05261
  
• Skilling, J. (1992). Bayesian Solution of Ordinary Differential Equations.” In Maximum Entropy and Bayesian Methods, 23–37. Dordrecht: Springer Netherlands.
• Briol, F.-X., Oates, C. J., Girolami, M., Osborne, M. A., and Sejdinovic, D. (2015). “Probabilistic Integration: A Role for Statisticians in Numerical Analysis?” arXiv:1512.00933 [stat.ML].
  arXiv: arXiv:1512.00933
  
• Chkrebtii, O. A., Campbell, D. A., Girolami, M. A., and Calderhead, B. (2016). “Bayesian Solution Uncertainty Quantification for Differential Equations.” Bayesian Analysis.
• Kersting, H. P. and Hennig, P. (2016). “Active Uncertainty Calibration in Bayesian ODE Solvers.” In Janzing and Ihlers (eds.), Uncertainty in Artificial Intelligence (UAI), volume 32.
• Schober, M., Särkkä, S., and Hennig, P. (2016). “A Probabilistic Model for the Numerical Solution of Initial Value Problems.” arXiv:1610.05261.
  arXiv: arXiv:1610.05261