Expanded uncertainty quantification in inverse problems: Hierarchical Bayes and empirical Bayes

By Alberto Malinverno, V. Briggs. 2004

265 citations recorded by the source corpus.

Subfields: Geophysics, Nuclear and High Energy Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bee1a6e90dd91754154aaa7fe286df7ffab99630

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Citations in the corpus

Inference of past climate from borehole temperature data using Bayesian reversible jump Markov chain Monte Carlo (2007, methodology): “Recent applications of RJ-MCMC and Bayesian inference to other geophysical problems include Malinverno (2000, 2002), Andersen et al. (2003), Malinverno & Briggs (2004), Malinverno & Leaney (2005), Stephenson et al. (2006) and Sambridge et al. (2006).”
Trans-dimensional inverse problems, model comparison and the evidence (2006, methodology): “The result (66) has been stated recently by Malinverno & Briggs (2004) in their Appendix B; however, the result is much older than this.”
Receiver function deconvolution using transdimensional hierarchical Bayesian inference (2014, methodology): “We present a method based on transdimensional (see Sambridge et al. 2013) hierarchical (Malinverno & Briggs 2004) Bayesian inference in which both the noise magnitude and noise spectral character are parameters in calculating the likelihood probability distribution .”
Markov chain Monte Carlo (MCMC) sampling methods to determine optimal models, model resolution and model choice for Earth Science problems (2009, background): “If there data errors are not well known, then these can be part of the inference process (e.g. Denison et al., 2002; Malinverno and Briggs, 2005; Malinverno and Parker, 2005).”
Transdimensional tomography with unknown data noise (2012, background): “…1536–1556 Geophysical Journal International C© 2012 RAS Downloaded from https://academic.oup.com/gji/article-abstract/189/3/1536/611337 by guest on 30 July 2018 is extended to hierarchical models which allow data error to be an unknown parameter (Malinverno & Briggs 2004; Malinverno & Parker 2006).”
Transdimensional inversion of receiver functions and surface wave dispersion (2012, methodology): “[20] In this work we address the issue of noise estimation with a Hierarchical approach [Malinverno and Briggs, 2004; Malinverno and Parker, 2006].”
Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters (2010, methodology): “The marginal likelihood function was previously derived in the geophysical literature for a single data set and a single prior PDF (e.g. Malinverno 2000; Malinverno & Briggs 2004; Sambridge et al. 2006).”
Estimation of trace gas fluxes with objectively determined basis functions using reversible jump Markov Chain Monte Carlo (2016, methodology): “…and q can be expressed in terms of the correlation timescale, τ , and δt following: This type of symmetric Toeplitz matrix has an explicit inverse (Malinverno and Briggs, 2004), which requires computation and storage that is proportional to N and is given The determinant of R can also be…”
A unified framework for multilevel uncertainty quantification in Bayesian inverse problems (2016, unknown): “Instead it can be viewed as leaving the prior for x1 incompletely specified [7], i.”
Uncertainty and nonuniqueness in linearized AVAZ for orthorhombic media (2015, methodology): “In this article, I study the inversion of linearized AVAZ for ORT media following the formulation and notation presented by Pšenčík and Martins (2001). In this study, I focus on inversion of the elastic parameters rather than the principal direction.”