447 citations · 3.6k across the 105 of their papers we have counts for
8 papers · 1 filter
Filtering Dynamical Systems Using Observations of Statistics
Eviatar Bach, Tim Colonius, Isabel Scherl +1
We consider the problem of filtering dynamical systems, possibly stochastic, using observations of statistics. Thus, the computational task is to estimate a time-evolving density $…
Inverse Problems and Data Assimilation
Daniel Sanz-Alonso, Andrew M. Stuart, Armeen Taeb
We provide a clear and concise introduction to the subjects of inverse problems and data assimilation, and their inter-relations. The first part of our notes covers inverse problem…
Dimension-Robust MCMC in Bayesian Inverse Problems
Victor Chen, Matthew M. Dunlop, Omiros Papaspiliopoulos +1
The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied…
Iterative Updating of Model Error for Bayesian Inversion
Daniela Calvetti, Matthew M. Dunlop, Erkki Somersalo +1
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may…
Probability Measures for Numerical Solutions of Differential Equations
Patrick R. Conrad, Mark Girolami, Simo Särkkä +2
In this paper, we present a formal quantification of epistemic uncertainty induced by numerical solutions of ordinary and partial differential equation models. Numerical solutions…
A Bayesian Level Set Method for Geometric Inverse Problems
Marco A. Iglesias, Yulong Lu, Andrew M. Stuart
We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the…