Bayesian inversion of hierarchical geostatistical models using a parallel-tempering sequential Gibbs MCMC

Reuschen, Sebastian; Xu, Teng; Nowak, Wolfgang

doi:10.1016/j.advwatres.2020.103614

Cited by 12 publications

(8 citation statements)

References 25 publications

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“…This makes it possible to have high acceptance rates

α

even for far jumps in the parameter space, which is synonymous with a high efficiency (see Section 2.7.2). We call this approach “sampling from the prior distribution” (Reuschen et al., 2020).…”

Section: Methodsmentioning

confidence: 99%

“…A combination of these approaches for binary classification problems with multi‐Gaussian heterogeneity was presented by Reuschen et al. (2020).…”

Section: Introductionmentioning

confidence: 99%

“…Hansen et al (2012) applied this idea to resample boxes of the parameter field in a binary classification problem. A combination of these approaches for binary classification problems with multi-Gaussian heterogeneity was presented by Reuschen et al (2020).…”

mentioning

confidence: 99%

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Efficient Discretization‐Independent Bayesian Inversion of High‐Dimensional Multi‐Gaussian Priors Using a Hybrid MCMC

Reuschen

Jobst

Nowak

2021

Water Resources Research

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“…This makes it possible to have high acceptance rates

α

Section: Methodsmentioning

confidence: 99%

“…A combination of these approaches for binary classification problems with multi‐Gaussian heterogeneity was presented by Reuschen et al. (2020).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Efficient Discretization‐Independent Bayesian Inversion of High‐Dimensional Multi‐Gaussian Priors Using a Hybrid MCMC

Reuschen

Jobst

Nowak

2021

Water Resources Research

Self Cite

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“…More refined geostatistical methods have been based on a clever combination of several developments of Markov random field theory. Along these lines, the work by Reuschen, Xu and Nowak [128] is noteworthy, since they used Bayesian inversion (based on Markov conditional independence) to develop a random field approach to hierarchical geostatistical models and used Gibbs sampling MCMC to solve them.…”

Section: Applications Of Mrfs In Statistics and Geostatisticsmentioning

confidence: 99%

Random Fields in Physics, Biology and Data Science

Hernández‐Lemus

2021

Front. Phys.

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A random field is the representation of the joint probability distribution for a set of random variables. Markov fields, in particular, have a long standing tradition as the theoretical foundation of many applications in statistical physics and probability. For strictly positive probability densities, a Markov random field is also a Gibbs field, i.e., a random field supplemented with a measure that implies the existence of a regular conditional distribution. Markov random fields have been used in statistical physics, dating back as far as the Ehrenfests. However, their measure theoretical foundations were developed much later by Dobruschin, Lanford and Ruelle, as well as by Hammersley and Clifford. Aside from its enormous theoretical relevance, due to its generality and simplicity, Markov random fields have been used in a broad range of applications in equilibrium and non-equilibrium statistical physics, in non-linear dynamics and ergodic theory. Also in computational molecular biology, ecology, structural biology, computer vision, control theory, complex networks and data science, to name but a few. Often these applications have been inspired by the original statistical physics approaches. Here, we will briefly present a modern introduction to the theory of random fields, later we will explore and discuss some of the recent applications of random fields in physics, biology and data science. Our aim is to highlight the relevance of this powerful theoretical aspect of statistical physics and its relation to the broad success of its many interdisciplinary applications.

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“…The Markov Chain Monte Carlo method (MCMC) was produced in the early 1950s. It is a Monte Carlo method (Monte Carlo) that is simulated by a computer under the framework of Bayesian theory (Reuschen et al, 2020). This method introduces the Markov process into the Monte Carlo simulation, realizes the dynamic simulation in which the sampling distribution changes with the simulation, and makes up for the traditional Monte Carlo integration that can only be statically simulated.…”

Section: Mcmcmentioning

confidence: 99%

Runoff forecast and analysis of the probability of dry and wet transition in the Hanjiang River Basin

Jin

Chen

Zhong

2021

Stoch Environ Res Risk Assess

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Runoff prediction has an important guiding role in the planning and management of regional water resources, flood prevention and drought resistance, and can effectively predict the risk of changes in regional water resources. This study used 12 runoff prediction methods to predict the runoff of four hydrological stations in the Hanjiang River Basin (HRB). Through the MCMC method, the HRB runoff probability conversion model from low to high (high to low) is constructed. The study found that the runoff of the HRB had a decreasing trend. In the mid-1980s, the runoff had a significant decreasing trend. The smoother the runoff changes, the easier it is to make accurate prediction. On the whole, the QS-MFM, MFM, MA-MFM, CES and DNN methods have strong generalization ability and can more accurately predict the runoff of the HRB. The Logistic model can accurately simulate the change of runoff status in the HRB. Among them, the HLT station has the fastest conversion rate of drought and flood, and the flow that generates floods is 6 times that of drought. The smaller the basin area, the larger the gap between drought and flood discharge. Overall, this research provides important technical support for the prediction of change in water resources and the transition probability from drought to flood in the HRB.

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Bayesian inversion of hierarchical geostatistical models using a parallel-tempering sequential Gibbs MCMC

Cited by 12 publications

References 25 publications

Efficient Discretization‐Independent Bayesian Inversion of High‐Dimensional Multi‐Gaussian Priors Using a Hybrid MCMC

Efficient Discretization‐Independent Bayesian Inversion of High‐Dimensional Multi‐Gaussian Priors Using a Hybrid MCMC

Random Fields in Physics, Biology and Data Science

Runoff forecast and analysis of the probability of dry and wet transition in the Hanjiang River Basin

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