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Inverse problems: A Bayesian perspective
TLDR
The Bayesian approach to regularization is reviewed, developing a function space viewpoint on the subject, which allows for a full characterization of all possible solutions, and their relative probabilities, whilst simultaneously forcing significant modelling issues to be addressed in a clear and precise fashion.
Multiscale Methods: Averaging and Homogenization
TLDR
This introduction to multiscale methods gives readers a broad overview of the many uses and applications of the methods, and sets the theoretical foundations of the subject area, and develops a unified approach to the simplification of a wide range of problems which possess multiple scales, via perturbation expansions.
MCMC Methods for Functions: ModifyingOld Algorithms to Make Them Faster
TLDR
An approach to modifying a whole range of MCMC methods, applicable whenever the target measure has density with respect to a Gaussian process or Gaussian random field reference measure, which ensures that their speed of convergence is robust under mesh refinement.
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 in
A First Course in Continuum Mechanics
TLDR
A concise account of various classic theories of fluids and solids for graduate students and advanced undergraduates, each chapter contains a wealth of exercises, with fully worked solutions to odd-numbered questions.
Optimal tuning of the hybrid Monte Carlo algorithm
TLDR
It is proved that, to obtain an O(1) acceptance probability as the dimension d of the state space tends to, the leapfrog step-size h should be scaled as h=l ×d−1/ 4, which means that in high dimensions, HMC requires O(d1/ 4 ) steps to traverse the statespace.
Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
TLDR
This work gives a convergence result for Euler--Maruyama requiring only that the SDE is locally Lipschitz and that the pth moments of the exact and numerical solution are bounded for some p >2 and shows that the optimal rate of convergence can be recovered if the drift coefficient is also assumed to behave like a polynomial.
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 numerical
Ensemble Kalman methods for inverse problems
TLDR
It is demonstrated 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, and that the accuracy is of the same order of magnitude as that achieve by the best approximation.
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