Bayes linear analysis for ordinary differential equations

[1]  Assyr Abdulle,et al.  Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration , 2018, Statistics and Computing.

[2]  C. J. Oates,et al.  A modern retrospective on probabilistic numerics , 2019, Statistics and Computing.

[3]  Simo Särkkä,et al.  Probabilistic solutions to ordinary differential equations as nonlinear Bayesian filtering: a new perspective , 2018, Statistics and Computing.

[4]  Peter Challenor,et al.  Emulating dynamic non-linear simulators using Gaussian processes , 2018, Comput. Stat. Data Anal..

[5]  Robert G. Aykroyd,et al.  Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment , 2017, Journal of the American Statistical Association.

[6]  T. J. Sullivan,et al.  Strong convergence rates of probabilistic integrators for ordinary differential equations , 2017, Statistics and Computing.

[7]  Mark A. Girolami,et al.  Bayesian Probabilistic Numerical Methods , 2017, SIAM Rev..

[8]  Ben Calderhead,et al.  Implicit Probabilistic Integrators for ODEs , 2018, NeurIPS.

[9]  Simo Särkkä,et al.  A probabilistic model for the numerical solution of initial value problems , 2016, Statistics and Computing.

[10]  Andrew M. Stuart,et al.  Statistical analysis of differential equations: introducing probability measures on numerical solutions , 2016, Statistics and Computing.

[11]  Martin Lysy.  Comment on Article by Chkrebtii, Campbell, Calderhead, and Girolami , 2016 .

[12]  Ben Calderhead,et al.  Probabilistic Linear Multistep Methods , 2016, NIPS.

[13]  Mark A. Girolami,et al.  Probabilistic Meshless Methods for Partial Differential Equations and Bayesian Inverse Problems , 2016, ArXiv.

[14]  Rolf Niedermeier,et al.  Enumerating maximal cliques in temporal graphs , 2016, 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM).

[15]  Philipp Hennig,et al.  Active Uncertainty Calibration in Bayesian ODE Solvers , 2016, UAI.

[16]  Michael A. Osborne,et al.  Probabilistic numerics and uncertainty in computations , 2015, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[17]  Jenný Brynjarsdóttir,et al.  Learning about physical parameters: the importance of model discrepancy , 2014 .

[18]  David Duvenaud,et al.  Probabilistic ODE Solvers with Runge-Kutta Means , 2014, NIPS.

[19]  M. Girolami,et al.  Bayesian Solution Uncertainty Quantification for Differential Equations , 2013 .

[20]  John M. Stockie,et al.  The Mathematics of Atmospheric Dispersion Modeling , 2011, SIAM Rev..

[21]  Ian Vernon,et al.  Galaxy formation : a Bayesian uncertainty analysis. , 2010 .

[22]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[23]  Pinar Heggernes,et al.  Sequential and parallel triangulating algorithms for Elimination Game and new insights on Minimum Degree , 2008, Theor. Comput. Sci..

[24]  Frédéric Cazals,et al.  A note on the problem of reporting maximal cliques , 2008, Theor. Comput. Sci..

[25]  Vibration of bell towers excited by bell ringing - a new approach to analysis , 2008 .

[26]  A. Iserles.  A First Course in the Numerical Analysis of Differential Equations: Gaussian elimination for sparse linear equations , 2008 .

[27]  David Wooff,et al.  Bayes Linear Statistics: Theory and Methods , 2007 .

[28]  G. Vallis.  Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation , 2017 .

[29]  Pinar Heggernes,et al.  Minimal triangulations of graphs: A survey , 2006, Discret. Math..

[30]  Michael Goldstein,et al.  Probabilistic Formulations for Transferring Inferences from Mathematical Models to Physical Systems , 2005, SIAM J. Sci. Comput..

[31]  Thore Graepel,et al.  Solving Noisy Linear Operator Equations by Gaussian Processes: Application to Ordinary and Partial Differential Equations , 2003, ICML.

[32]  Michael Goldstein,et al.  Bayesian Forecasting for Complex Systems Using Computer Simulators , 2001 .

[33]  Jiri Blazek,et al.  Computational Fluid Dynamics: Principles and Applications , 2001 .

[34]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[35]  Darren J. Wilkinson,et al.  Bayes linear analysis for graphical models: The geometric approach to local computation and interpretive graphics , 2000, Stat. Comput..

[36]  Klaus Ritter,et al.  Bayesian numerical analysis , 2000 .

[37]  Michael I. Jordan.  Graphical Models , 2003 .

[38]  Arieh Iserles,et al.  A First Course in the Numerical Analysis of Differential Equations: The diffusion equation , 2008 .

[39]  F. Pukelsheim.  The Three Sigma Rule , 1994 .

[40]  J. Skilling.  Bayesian Solution of Ordinary Differential Equations , 1992 .

[41]  A. O'Hagan,et al.  Bayes–Hermite quadrature , 1991 .

[42]  R. LeVeque.  Numerical methods for conservation laws , 1990 .

[43]  Anthony O'Hagan,et al.  Monte Carlo is fundamentally unsound , 1987 .

[44]  J. W. Humberston.  Classical mechanics , 1980, Nature.

[45]  C. Bron,et al.  Algorithm 457: finding all cliques of an undirected graph , 1973 .

[46]  F. M. Larkin.  Gaussian measure in Hilbert space and applications in numerical analysis , 1972 .

[47]  J. Butcher.  Coefficients for the study of Runge-Kutta integration processes , 1963, Journal of the Australian Mathematical Society.