A role for symmetry in the Bayesian solution of differential equations

DOI10.1214/19-BA1183zbMath1483.65021arXiv1906.10564WikidataQ115240827 ScholiaQ115240827MaRDI QIDQ2057339

Junyang Wang, Chris J. Oates, Jon Cockayne

Publication date: 6 December 2021

Published in: Bayesian Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.10564

zbMATH Keywords

ordinary differential equationsLie groupsprobabilistic numerics

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Bayesian inference (62F15) Numerical methods for initial value problems involving ordinary differential equations (65L05) Probabilistic methods, stochastic differential equations (65C99)

Related Items (7)

Randomised one-step time integration methods for deterministic operator differential equations ⋮ Strong convergence rates of probabilistic integrators for ordinary differential equations ⋮ Adaptive step-size selection for state-space probabilistic differential equation solvers ⋮ Probabilistic solutions to ordinary differential equations as nonlinear Bayesian filtering: a new perspective ⋮ A modern retrospective on probabilistic numerics ⋮ Bayesian ODE solvers: the maximum a posteriori estimate ⋮ Bayesian numerical methods for nonlinear partial differential equations

Uses Software

• mctoolbox

Cites Work

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• Bayesian solution uncertainty quantification for differential equations
• Emergence of the theory of Lie groups. An essay in the history of mathematics 1869--1926
• Symmetry and integration methods for differential equations
• Statistical analysis of differential equations: introducing probability measures on numerical solutions
• Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration
• Convergence rates of Gaussian ODE filters
• Strong convergence rates of probabilistic integrators for ordinary differential equations
• Adaptive step-size selection for state-space probabilistic differential equation solvers
• Probabilistic solutions to ordinary differential equations as nonlinear Bayesian filtering: a new perspective
• A modern retrospective on probabilistic numerics
• Rejoinder: ``Probabilistic integration: a role in statistical computation?
• A probabilistic model for the numerical solution of initial value problems
• Gaussian measure in Hilbert space and applications in numerical analysis
• Increasing horizontal resolution in numerical weather prediction and climate simulations: illusion or panacea?
• Perspectives on information-based complexity
• A Posteriori Error Bounds and Global Error Control for Approximation of Ordinary Differential Equations
• Conditioning as disintegration
• Finite-Dimensional Gaussian Approximation with Linear Inequality Constraints
• Random Forward Models and Log-Likelihoods in Bayesian Inverse Problems
• Philosophy and the practice of Bayesian statistics
• Accuracy and Stability of Numerical Algorithms
• Bayesian Probabilistic Numerical Methods
• Probabilistic numerics and uncertainty in computations

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