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Inverse problems: A Bayesian perspective
  • A. Stuart
  • Mathematics, Computer Science
  • Acta Numerica
  • 1 May 2010
The subject of inverse problems in differential equations is of enormous practical importance, and has also generated substantial mathematical and computational innovation. Expand
Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise
The ergodic properties of SDEs, and various time discretizations for SDEs, are studied. The ergodicity of SDEs is established by using techniques from the theory of Markov chains on general stateExpand
Multiscale Methods: Averaging and Homogenization
This introduction to multiscale methods gives readers a broad overview of the many uses and applications of the methods. Expand
MCMC Methods for Functions: ModifyingOld Algorithms to Make Them Faster
Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes.Expand
A First Course in Continuum Mechanics
A concise account of various classic theories of fluids and solids, this book is for courses in continuum mechanics. Expand
Dynamical Systems And Numerical Analysis
This book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numericalExpand
The Bayesian Approach to Inverse Problems
These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems inExpand
Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
We show that an implicit variant of Euler--Maruyama converges if the diffusion coefficient is globally Lipschitz, but the drift coefficient satisfies only a one-sided Lipschnitz condition; this is achieved by showing that the implicit method has bounded moments and may be viewed as an approximation to a perturbed SDE of the same form. Expand
Optimal tuning of the hybrid Monte Carlo algorithm
We investigate the properties of the Hybrid Monte Carlo algorithm (HMC) in high dimensions. HMC develops a Markov chain reversible w.r.t. a given target distribution . by using separable HamiltonianExpand
Ensemble Kalman methods for inverse problems
We show that the ensemble Kalman method for inverse problems provides a derivative-free optimization method with comparable accuracy to that achieved by traditional least-squares approaches. Expand