Sampling Algorithms for Discrete Markov Random Fields and Related Graphical Models

Izenman, Alan Julian

doi:10.1080/01621459.2021.1898410

Cited by 4 publications

(3 citation statements)

References 93 publications

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“…To reproduce observed melt pond spatial configurations, Ma et al (2019) created a model akin the random field Ising model (RFIM; Krapivsky et al, 2010). The “Ising model” has been widely used in the theory of lattice models of statistical mechanics as a special case of Markov random fields (MRFs) or Markov networks (Izenman, 2021).…”

Section: Example: Sea Ice Emulatormentioning

confidence: 99%

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Statistical mechanics in climate emulation: Challenges and perspectives

Sudakow

Pokojovy

Lyakhov

2022

Environ. Data Science

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Climate emulators are a powerful instrument for climate modeling, especially in terms of reducing the computational load for simulating spatiotemporal processes associated with climate systems. The most important type of emulators are statistical emulators trained on the output of an ensemble of simulations from various climate models. However, such emulators oftentimes fail to capture the “physics” of a system that can be detrimental for unveiling critical processes that lead to climate tipping points. Historically, statistical mechanics emerged as a tool to resolve the constraints on physics using statistics. We discuss how climate emulators rooted in statistical mechanics and machine learning can give rise to new climate models that are more reliable and require less observational and computational resources. Our goal is to stimulate discussion on how statistical climate emulators can further be improved with the help of statistical mechanics which, in turn, may reignite the interest of statistical community in statistical mechanics of complex systems.

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Section: Example: Sea Ice Emulatormentioning

confidence: 99%

“…For most MRFs, there is no closed form expression for the partition function and, therefore, direct sampling is not feasible. However, we can produce (approximate) samples from these models using MCMC simulations (Izenman, 2021).…”

Section: Example: Sea Ice Emulatormentioning

confidence: 99%

Statistical mechanics in climate emulation: Challenges and perspectives

Sudakow

Pokojovy

Lyakhov

2022

Environ. Data Science

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“…After L = 1, 000, 000 iterations, the last result is a sample x we use. One can read [18] for more details of sampling from Ising model. 4.2.…”

Section: 1mentioning

confidence: 99%

Variational Bayes algorithm and posterior consistency of Ising model parameter estimation

Kim¹,

Bhattacharya²,

Maiti³

2021

Preprint

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Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant in the likelihood. Here, we use a pseudo-likelihood instead to study the Bayesian estimation of two-parameter, inverse temperature, and magnetization, Ising model with a fully specified coupling matrix. We develop a computationally efficient variational Bayes procedure for model estimation. Under the Gaussian mean-field variational family, we derive posterior contraction rates of the variational posterior obtained under the pseudolikelihood. We also discuss the loss incurred due to variational posterior over true posterior for the pseudo-likelihood approach. Extensive simulation studies validate the efficacy of mean-field Gaussian and bivariate Gaussian families as the possible choices of the variational family for inference of Ising model parameters.

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