Markov chain Monte Carlo Using an Approximation

By J. Christen, Colin Fox. 2005

337 citations recorded by the source corpus.

Subfields: Applied Mathematics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/7e0f1514ae7bae557116e8b689d1fb2b2c08960c

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In Applied Mathematics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Bayesian calibration of a large‐scale geothermal reservoir model by a new adaptive delayed acceptance Metropolis Hastings algorithm (2011, methodology): “ADAMH is always statistically less efficient than the standard MH [Christen and Fox, 2005], because it requires more iterations to generate a statistically independent sample than the standard MH.”
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],”
Efficient posterior exploration of a high‐dimensional groundwater model from two‐stage Markov chain Monte Carlo simulation and polynomial chaos expansion (2013, methodology): “Note however, that this gain in computational effort compared to standard MCMC simulation schemes comes at the expense of a potential increase in autocorrelation between the posterior samples [Christen and Fox, 2005; Cui et al., 2011].”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, methodology): “In principle, the proposals in the context of delayed rejection MCMC, just as in delayed acceptance MCMC, can also be derived from models with different fidelities and costs (although we are not aware of such implementations in the literature that predate the work by [44, 73]).”
Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems [Chapter 7] (2010, background): “Christen and Fox (2005) use a local linear approximation of the forward model to improve the acceptance probability of proposed moves, reducing the number of times the likelihood must be evaluated with the full forward model.”
Optimal Model Management for Multifidelity Monte Carlo Estimation (2016, methodology): “In statistical inference, two-stage Markov chain Monte Carlo techniques rely on surrogate models to decide whether a proposed sample is further processed by the high-fidelity model, discarded, or used to adapt the surrogate model [14, 19, 17].”
Review of multi-fidelity models (2016, methodology): “Several studies illustrate the diversity of applications and methods within MFHMs. Christen and Fox employed LFMs in initial Markov Chain Monte Carlo sampling and shifted to HFMs when specific criteria were met [44].”
Efficient Bayesian inference of subsurface flow models using nested sampling and sparse polynomial chaos surrogates (2014, methodology): “The proposed algorithm is a two-stage MCMC algorithm [17,6] where a proxy model is built using polynomial chaos to filter out rejected samples.”
Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems (2018, positive): “To improve this, one can use two-stage MCMC simulations that leverage low-ﬁdelity models to speed up the sampling as in[4, 9], or one can continually reﬁne the surrogate during MCMC sampling as in [6, 7, 8, 20].”