Accelerating MCMC algorithms

Robert, Christian P.; Elvira, Vı́ctor; Tawn, Nicholas G.; Wu, Changye

doi:10.1002/wics.1435

Cited by 114 publications

(72 citation statements)

References 98 publications

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“…Separate pooled meta-analyses of survival benefits associated with GTR of glioblastoma were determined for publications contributed by members of genealogy A (neurosurgeons) and B (radiation oncologists), as well as non-genealogy members. To determine whether the observed disparity was random, we performed χ 2 -based Monte Carlo simulations with a pvalue based on 10,000 simulations [30]. Monte Carlo simulations were executed by randomly selecting 6 and 20 studies from all articles identified in our literature search (matching the number of articles contributed by the radiation oncology genealogy and neurosurgery genealogy, respectively).…”

Section: Discussionmentioning

confidence: 99%

Association between medical academic genealogy and publication outcome: impact of unconscious bias on scientific objectivity

et al. 2019

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Background: Our previous studies suggest that the training history of an investigator, termed "medical academic genealogy", influences the outcomes of that investigator's research. Here we use meta-analysis and quantitative statistical modeling to determine whether such effects contribute to systematic bias in published conclusions. Methods: 108 articles were identified through a comprehensive search of the high-grade glioma (HGG) surgical resection literature. Analysis was performed on the 70 articles with sufficient data for meta-analysis. Pooled estimates were generated for key academic genealogies. Monte Carlo simulations were performed to determine whether the effects attributed to genealogy alone can arise due to chance alone. Results: Meta-analysis of the HGG literature without consideration for academic medical genealogy revealed that gross total resection (GTR) was associated with a significant decrease in

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Section: Discussionmentioning

confidence: 99%

Association between medical academic genealogy and publication outcome: impact of unconscious bias on scientific objectivity

et al. 2019

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“…It is important to note that the number of training parameters does not increase with the dimensionality of the problem but only depends on the number of categories (i.e., labels) and features used in the model. The main challenge in extending the current model to 3-D will be the increase in computational time for both training and simulation steps, which could be addressed by implementing more advanced optimization and sampling methods such as incremental gradient decent (Mokhtari et al, 2018) and parallel multiple proposal MCMC algorithms (Calderhead, 2014;Robert et al, 2018).…”

Section: Water Resources Researchmentioning

confidence: 99%

Subsurface Source Zone Characterization and Uncertainty Quantification Using Discriminative Random Fields

Arshadi

Kaluza

Miller

et al. 2020

Water Resources Research

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A novel statistical approach is developed and implemented for the stochastic reconstruction of nonaqueous phase liquid (NAPL) source zone realizations and the quantification of source zone metrics and associated uncertainty. The approach employs discriminative random field (DRF) models, to simulate the spatial distributions and relationships among source zone properties (i.e., permeability, NAPL saturation, and aqueous concentration distributions) consistent with commonly collected field data. Application of DRF models requires a limited number of full‐scale simulations to train the model parameters. Monte Carlo sampling methods based on these trained models then provide an efficient method to generate contaminant mass realizations conditioned on measured boreholes, bypassing the need to run computationally intensive, partial differential equation‐based simulations of physical flow and transport. Postprocessing of these realizations yields approximations of uncertainty to inform further sampling for characterization and remediation. The reconstructed contaminant mass realizations provide sufficient information for calculating averaged characterization metrics, such as total contaminant mass and pool fraction, used to predict source zone longevity, mass recovery behavior, and remedial performance. The model performance is evaluated through comparisons of these predicted source zone metrics with those obtained from the “true” mass distributions generated with validated flow and transport models. These comparisons clearly demonstrate that stochastic application of a DRF model can reconstruct realistic saturation and concentration fields, conditioned to borehole data at different times. The present study should be viewed as the first step in generating a three‐dimensional characterization tool that can be applied over a wide range of conditions observed at contaminated sites.

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“…This algorithm was shown to be capable for Bayesian inversion of multi‐Gaussian subsurface properties in many applications (e.g., Cotter et al., 2013; Hu et al., 2017; Iglesias et al., 2012). Still, when pCN‐MCMC explores the target posterior distribution, it may still need a long chain and it is still difficult to explore a large potential model space since the MCMC simulation proceeds by local jumps in the vicinity of the current solutions (Robert et al., 2018). Parallel tempering can handle the dilemma with exploring large model spaces and can improve the efficiency of exploring the target posterior by exchange swaps between cold chains and hot chains.…”

Section: Introductionmentioning

confidence: 99%

Preconditioned Crank‐Nicolson Markov Chain Monte Carlo Coupled With Parallel Tempering: An Efficient Method for Bayesian Inversion of Multi‐Gaussian Log‐Hydraulic Conductivity Fields

Reuschen

Nowak

et al. 2020

Water Resources Research

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Geostatistical inversion with quantified uncertainty for nonlinear problems requires techniques for providing conditional realizations of the random field of interest. Many first‐order second‐moment methods are being developed in this field, yet almost impossible to critically test them against high‐accuracy reference solutions in high‐dimensional and nonlinear problems. Our goal is to provide a high‐accuracy reference solution algorithm. Preconditioned Crank‐Nicolson Markov chain Monte Carlo (pCN‐MCMC) has been proven to be more efficient in the inversion of multi‐Gaussian random fields than traditional MCMC methods; however, it still has to take a long chain to converge to the stationary target distribution. Parallel tempering aims to sample by communicating between multiple parallel Markov chains at different temperatures. In this paper, we develop a new algorithm called pCN‐PT. It combines the parallel tempering technique with pCN‐MCMC to make the sampling more efficient, and hence converge to a stationary distribution faster. To demonstrate the high‐accuracy reference character, we test the accuracy and efficiency of pCN‐PT for estimating a multi‐Gaussian log‐hydraulic conductivity field with a relative high variance in three different problems: (1) in a high‐dimensional, linear problem; (2) in a high‐dimensional, nonlinear problem and with only few measurements; and (3) in a high‐dimensional, nonlinear problem with sufficient measurements. This allows testing against (1) analytical solutions (kriging), (2) rejection sampling, and (3) pCN‐MCMC in multiple, independent runs, respectively. The results demonstrate that pCN‐PT is an asymptotically exact conditional sampler and is more efficient than pCN‐MCMC in geostatistical inversion problems.

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Accelerating MCMC algorithms

Cited by 114 publications

References 98 publications

Association between medical academic genealogy and publication outcome: impact of unconscious bias on scientific objectivity

Association between medical academic genealogy and publication outcome: impact of unconscious bias on scientific objectivity

Subsurface Source Zone Characterization and Uncertainty Quantification Using Discriminative Random Fields

Preconditioned Crank‐Nicolson Markov Chain Monte Carlo Coupled With Parallel Tempering: An Efficient Method for Bayesian Inversion of Multi‐Gaussian Log‐Hydraulic Conductivity Fields

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