Trans-dimensional inverse problems, model comparison and the evidence

By Malcolm Sambridge, K. Gallagher, Andrew Jackson, P. Rickwood. 2006

323 citations recorded by the source corpus.

Subfields: Environmental Engineering, Geophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/33269bc26eabbee8442984dcddf7bc8e170b6dfc

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Citations in the corpus

Data‐driven spatial b value estimation with applications to California seismicity: To b or not to b (2015, methodology): “The method bears similarities with, and is in fact inspired by, the concept of transdimensional inference developed by Sambridge and others [Sambridge et al., 2006, 2013; Bodin and Sambridge, 2009].”
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).”
A trans-dimensional Bayesian Markov chain Monte Carlo algorithm for model assessment using frequency-domain electromagnetic data (2011, background): “…2003), geological mapping (Gabriel et al. 2003; Best et al. 2006), groundwater (Fitterman & Deszcz-Pan 1998; Roettger et al. 2005; Lipinski et al. 2008), agriculture (Allred et al. 2005; Daniels et al. 2008; Sams et al. 2008) and environmental studies (Siemon et al. 2002; Al-Fouzan et al. 2004).”
Estimation of trace gas fluxes with objectively determined basis functions using reversible jump Markov Chain Monte Carlo (2016, methodology): “However, Bayes theorem follows the principle of Occam’s razor, in that given a choice between a complicated and simple solution that provide similar ﬁts to the data, the simpler one will be favoured (Sambridge et al., 2006).”
Markov chain Monte Carlo (MCMC) sampling methods to determine optimal models, model resolution and model choice for Earth Science problems (2009, methodology): “The 2nd term on the right, p(djH) is sometimes referred to as the evidence (e.g. Mackay, 2003; Sambridge et al., 2006), and the evidence measures how well a given hypothesis can explain the data.”
Seismic tomography with the reversible jump algorithm (2009, methodology): “From the modelling of the Rayleigh wave derivatives at a period of 5 s, the traveltime used here are mostly sensitive to the structure in the first 3 km of he crust (Saygin 2007).”
Transdimensional tomography with unknown data noise (2012, background): “Here it is based on a Gaussian distribution which quantifies the agreement between simulated and observed data (Sambridge et al. 2006): p(d|m) = 1√ (2π )N |Ce| ×exp { − 1 2 ( [g(m) − d]T C−1e [g(m) − d] )} , (2) where g(m) is the vector (of length N) of traveltimes estimated for the seismic model…”