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- Youssef M. Marzouk, Habib N. Najm, Larry A. Rahn
- J. Comput. Physics
- 2007

We present a reformulation of the Bayesian approach to inverse problems, that seeks to accelerate Bayesian inference by using polynomial chaos (PC) expansions to represent random variables. Evaluation of integrals over the unknown parameter space is recast, more efficiently, as Monte Carlo sampling of the random variables underlying the PC expansion. We… (More)

- Tarek A. El-Moselhy, Youssef M. Marzouk
- J. Comput. Physics
- 2012

We present a new approach to Bayesian inference that entirely avoids Markov chain simulation, by constructing a map that pushes forward the prior measure to the posterior measure. Existence and uniqueness of a suitable measure-preserving map is established by formulating the problem in the context of optimal transport theory. We discuss various means of… (More)

- Patrick R. Conrad, Youssef M. Marzouk
- SIAM J. Scientific Computing
- 2013

Polynomial approximations of computationally intensive models are central to uncertainty quantification. This paper describes an adaptive method for nonintrusive pseudospectral approximation, based on Smolyak’s algorithm with generalized sparse grids. We rigorously analyze and extend the nonadaptive method proposed in [P. G. Constantine, M. S. Eldred, and… (More)

The intrinsic dimensionality of an inverse problem is affected by prior information, the accuracy and number of observations, and the smoothing properties of the forward operator. From a Bayesian perspective, changes from the prior to the posterior may, in many problems, be confined to a relatively lowdimensional subspace of the parameter space. We present… (More)

- Youssef M. Marzouk, Habib N. Najm
- J. Comput. Physics
- 2009

We consider a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a spatial or temporal field, endowed with a hierarchical Gaussian process prior. Computational challenges in this construction arise from the need for repeated evaluations of the forward model (e.g., in the context of Markov chain Monte Carlo) and are compounded… (More)

- Xun Huan, Youssef M. Marzouk
- J. Comput. Physics
- 2013

The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models;… (More)

- Tiangang Cui, Kody J. H. Law, Youssef M. Marzouk
- J. Comput. Physics
- 2016

Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that, in principle, can be described as functions. This work introduces a family of Markov chain Monte Carlo (MCMC) samplers that can adapt to the particular structure of a posterior distribution over functions. Two distinct lines of research… (More)

We present a Bayesian approach for estimating transmission chains and rates in the Abakaliki smallpox epidemic of 1967. The epidemic affected 30 individuals in a community of 74; only the dates of appearance of symptoms were recorded. Our model assumes stochastic transmission of the infections over a social network. Distinct binomial random graphs model… (More)

- Akil Narayan, Youssef M. Marzouk, Dongbin Xiu
- J. Comput. Physics
- 2012

Data assimilation is an essential tool for predicting the behavior of real physical systems given approximate simulation models and limited observations. For many complex systems, there may exist several models, each with different properties and predictive capabilities. It is desirable to incorporate multiple models into the assimilation procedure in order… (More)

- Alessio Spantini, Antti Solonen, Tiangang Cui, James Martin, Luis Tenorio, Youssef M. Marzouk
- SIAM J. Scientific Computing
- 2015