A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion

By James Martin, Lucas C. Wilcox, Carsten Burstedde, Omar Ghattas. SIAM Journal on Scientific Computing, 2012

469 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5a88c9ffcfc30745cbd00403385418ee3984883c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Bayesian inference with optimal maps (2011, methodology): “A non-exhaustive list of recent methodological advances includes adaptivity based on past samples [11, 12], Langevin methods [13, 14], the use of Hessian information [15] and Hessians with low-rank structure [16], Hamiltonian dynamics [17], the exchange of information among multiple chains [18– 20],”
SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence (2020, methodology): “…understanding of algorithms based on Langevin diﬀusions [Dal17a,Ber18,CB18,Wib18,DMM19,VW19], but has also fueled the discovery of new MCMC algorithms inspired by the diverse and powerful optimization toolbox [MWBG12, SBCR16, CCBJ18, Ber18, HKRC18, Wib18, MCC + 19, Wib19, CLL + 20, DRD20, ZPFP20].”
An introduction to sampling via measure transport (2016, background): “While these eﬀorts are too diverse to summarize easily, they often rest on the design of improved (and structure-exploiting) proposal mechanisms within the algorithms [37, 3, 26, 22, 62, 53, 34, 24].”
Structured Bayesian Gaussian process latent variable model: applications to data-driven dimensionality reduction and high-dimensional inversion (2018, background): “Examples of inverse problems include parameter calibration [1, 2], subsurface flow [3, 4], ocean dynamics [5], remote sensing [6], seismic inversion [7], and others.”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, methodology): “MCMC methods are a popular way to sample from the posterior distribution and have been studied extensively [178, 90, 139, 80, 50, 137, 53, 52]; see also the books [77, 130].”
Fast derivatives of likelihood functionals for ODE based models using adjoint-state method (2016, methodology): “The ﬁdelity between the data and the PDE-based model is measured in a Lebesgue space L p − norm, particularly in L 2 sense, as is also the case of the above mentioned paper (Martin et al., 2012).”