BayesianPosteriorTargeted

Bayesian posterior targeted from El Gammal et al. 2023.

Overview

The BayesianPosteriorTargeted acquisition function is proposed by (El Gammal et al., 2023) for Bayesian inverse UQ applications. The functional form is given by:

$(1)var element = document.getElementById("moose-equation-e5d7886c-3fdb-4eac-9648-e4d700906d22");katex.render(" a(\\pmb{x}) = \\exp{(2\\psi \\mu)}~(\\exp{(\\sigma)}-1)", element, {displayMode:true,throwOnError:false});$

where, $var element = document.getElementById("moose-equation-cee3485f-8869-46fa-a3d7-30a8e4e466ac");katex.render("\\psi", element, {displayMode:false,throwOnError:false});$ is a factor to boost the exploratory behavior and set to $var element = document.getElementById("moose-equation-57d87e0f-51f6-4f3a-a0c9-32f08b765ecb");katex.render("N^{-0.85}", element, {displayMode:false,throwOnError:false});$ ( $var element = document.getElementById("moose-equation-1a6147da-c22f-4a7d-8d4d-0bf709400c53");katex.render("N", element, {displayMode:false,throwOnError:false});$ is the number of model parameters), $var element = document.getElementById("moose-equation-d07f4d4b-80bd-4e9e-8c9a-e7a3a3b8dac5");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ is the Gaussian process mean prediction, and $var element = document.getElementById("moose-equation-3ef6ac6b-541b-4b2f-828b-cc283620fb6d");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ is the Gaussian process standard deviation.

Input Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.

References

J. El Gammal, N. Schöneberg, J. Torrado, and C. Fidler. Fast and robust bayesian inference using gaussian processes with gpry. Journal of Cosmology and Astroparticle Physics, 2023(10):021, 2023.

@article{Gammal2023al,
    author = "El Gammal, J. and Schöneberg, N. and Torrado, J. and Fidler, C.",
    title = "Fast and robust Bayesian inference using Gaussian processes with GPry",
    journal = "Journal of Cosmology and Astroparticle Physics",
    volume = "2023",
    number = "10",
    pages = "021",
    year = "2023"
}

Overview
Input Parameters
References