A stochastic collocation approach to Bayesian inference in inverse problems

By Youssef M. Marzouk, Dongbin Xiu. 2009

314 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/20e497afcbd0222d548f8215c7c45ea2b0dbe8d6

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Citations in the corpus

Simulation-based optimal Bayesian experimental design for nonlinear systems (2011, methodology): “, [56, 57, 58]), and this is the approach we shall use.”
Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems (2018, unknown): “Many surrogate modeling methods have been successfully employed in this context, for example, projection-type reduced order models [2, 11, 12, 16, 21], polynomial chaos (PC) [24, 26, 27, 28, 41] and Gaussian process regression [18, 36, 38], to name a few.”
Efficient posterior exploration of a high‐dimensional groundwater model from two‐stage Markov chain Monte Carlo simulation and polynomial chaos expansion (2013, methodology): “Those studies that have used gPC with MCMC simulation [Dostert et al., 2009; Marzouk and Najm, 2009; Marzouk and Xiu, 2009] were limited to relatively simple case studies, often involving synthetic data, low-dimensional models and simple search methods.”
An adaptive sparse‐grid high‐order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling (2013, methodology): “The Bayesian method is one of the most widely utilized approaches for quantifying parametric uncertainty [Kitanidis, 1986; Box and Tiao, 1992; Ezzedine et al., 1999; Beck and Au, 2002; Marshall et al., 2005; Marzouk et al., 2007; Ma and Zabaras, 2009; Marzouk and Xiu, 2009; Allaire and Willcox, 2010”
Probabilistic Meshless Methods for Partial Differential Equations and Bayesian Inverse Problems (2016, methodology): “eviation between derivatives of this approximate solution and the derivative values that are required; see [12, 21, 35, 59] and the references therein. Closer in spirit to the approach pursued below, [51] used polynomial chaos expansions to approximate the likelihood, treating the mapping from param”
Adaptive Gaussian Process Approximation for Bayesian Inference with Expensive Likelihood Functions (2017, methodology): “Namely, we consider the kinetics of a genetic toggle switch, which was ﬁrst Right: the KLD between from the true posterior to the GP approximation plotted against the number of iterations. studied in [2] and later numerically investigated in [13].”
Bayesian inference with optimal maps (2011, background): “As in [54], we would like to infer the six model parameters α1, α2, β, γ, η and κ.”
Stochastic Collocation Algorithms Using l1-Minimization for Bayesian Solution of Inverse Problems (2015, methodology): “Here, we compute the polynomial coefficients with a level-6 sparse grid based on Clenshaw–Curtis quadrature [28], resulting in 321 true model evaluations—about 10 times as many as the L1-SCM.”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, background): “We refer to [130, 208, 209, 139, 207] for an introduction to polynomial chaos expansion and further details.”
Efficient Bayesian inference of subsurface flow models using nested sampling and sparse polynomial chaos surrogates (2014, methodology): “Marzouk and Xiu [22] introduced a stochastic collocation approach to Bayesian inference where a polynomial approximation of the forward solution is constructed over the prior distribution support.”
Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems [Chapter 7] (2010, background): “Error analysis of the Bayesian stochastic spectral framework (Marzouk and Xiu 2009) has reinforced this flexibility.”
A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion (2012, methodology): “This stochastic problem is more expensive than the original forward problem, but once obtained, the solution can be used to construct a surrogate for the posterior distribution, which can be evaluated repeatedly at negligible cost, making it ideal for MCMC sampling [30, 32].”