Markov chain Monte Carlo (MCMC) sampling methods to determine optimal models, model resolution and model choice for Earth Science problems

被引:234
作者
Gallagher, Kerry [1 ]
Charvin, Karl [2 ]
Nielsen, Soren [3 ]
Sambridge, Malcolm [4 ]
Stephenson, John [5 ]
机构
[1] Univ Rennes, F-35042 Rennes, France
[2] Univ London Imperial Coll Sci Technol & Med, Dept Earth Sci & Engn, London SW7 2AS, England
[3] Univ Aarhus, Dept Earth Sci, Aarhus, Denmark
[4] Australian Natl Univ, Res Sch Earth Sci, Canberra, ACT 0200, Australia
[5] BP, Sunbury On Thames TW16 7LN, Middx, England
基金
英国自然环境研究理事会;
关键词
Markov chain Monte Carlo; Inversion; Optimisation; LOW-TEMPERATURE THERMOCHRONOLOGY; HEAT-FLOW HISTORIES; INVERSE PROBLEMS; STRATEGIES;
D O I
10.1016/j.marpetgeo.2009.01.003
中图分类号
P [天文学、地球科学];
学科分类号
07 ;
摘要
We present an overview of Markov chain Monte Carlo, a sampling method for model inference and uncertainty quantification. We focus on the Bayesian approach to MCMC, which allows LIS to estimate the posterior distribution of model parameters, without needing to know the normalising constant in Bayes' theorem. Given an estimate of the posterior, we can then determine representative models (such as the expected model, and the maximum posterior probability model), the probability distributions for individual parameters, and the uncertainty about the predictions from these models. We also consider variable dimensional problems in which the number of model parameters is unknown and needs to be inferred. Such problems can be addressed with reversible jump (RJ) MCMC. This leads LIS to model choice, where we may want to discriminate between models or theories of differing complexity. For problems where the models are hierarchical (e.g. similar structure but with a different number of parameters), the Bayesian approach naturally selects the simpler models. More complex problems require an estimate of the normalising constant in Bayes' theorem (also known as the evidence) and this is difficult to do reliably for high dimensional problems. We illustrate the applications of RJMCMC with 3 examples from our earlier working involving modelling distributions of geochronological age data, inference of sea-level and sediment supply histories from 2D stratigraphic cross-sections, and identification of spatially discontinuous thermal histories from a Suite of apatite fission track samples distributed in 3D. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码:525 / 535
页数:11
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