Data-free inference of the joint distribution of uncertain model parameters

Berry, Robert Dan; Najm, Habib N.; Debusschere, Bert; Marzouk, Youssef; Adalsteinsson, Helgi

doi:10.1016/j.jcp.2011.10.031

Cited by 20 publications

(38 citation statements)

References 30 publications

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“…This is also called linear average pooling. One disadvantage of linear pooling is that it is not externally Bayesian [3,12], i.e., Bayesian updating and pooling do not commute, with the result that each consistent posterior has to be computed individually from each consistent data set, and saved, before proceeding to pooling. This can be quite inefficient.…”

Section: Entropic Inferencementioning

confidence: 99%

“…As already indicated, an important characteristic of logarithmic (or log for short) average pooling is that it is externally Bayesian [3,12]. This means one can log pool the individual posteriors or, equivalently, calculate the posterior based on the log pooled likelihoods.…”

Section: Entropic Inferencementioning

confidence: 99%

“…For example, Berry et al introduced a weight function [3] that penalized certain quantiles of the observed statistics, using the KL divergence pseudo-metric. We proceed in a similar manner.…”

Section: Consistent Data Sets and Approximate Bayesian Computationmentioning

confidence: 99%

“…; p M g, where p i Á p.xjy i / [3]. In this context, consistency is used to mean consistency with respect to the given information I , i.e., consistent data samples are samples from the data density p.yjI /.…”

Section: Algorithmic Structurementioning

confidence: 99%

“…In this context, consistency is used to mean consistency with respect to the given information I , i.e., consistent data samples are samples from the data density p.yjI /. Further, as indicated above, pooling [3,13] provides a means of combining information from different sources, in the form of consistent posteriors p i , in a manner corresponding to the marginalization in Eq. (31), with optionally additional constraints.…”

Section: Algorithmic Structurementioning

confidence: 99%

See 4 more Smart Citations

Inference Given Summary Statistics

Najm¹,

Chowdhary²

2015

Handbook of Uncertainty Quantification

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Section: Entropic Inferencementioning

confidence: 99%

Section: Entropic Inferencementioning

confidence: 99%

Section: Consistent Data Sets and Approximate Bayesian Computationmentioning

confidence: 99%

Section: Algorithmic Structurementioning

confidence: 99%

Section: Algorithmic Structurementioning

confidence: 99%

See 3 more Smart Citations

Inference Given Summary Statistics

Najm¹,

Chowdhary²

2015

Handbook of Uncertainty Quantification

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Estimating reaction parameters in mechanism‐enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

et al. 2021

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In order to quantitatively predict nano-as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth.The Bayesian approach addresses the question of "how well do we know our parameters, along with their uncertainties?." The results reveal that Bayesian inversion statistical analysis on an example, prototype Ir 0 ð Þ n nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. The paper can also be seen as a tutorial with the additional goal of achieving a "Gold Standard" Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.

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Inference Given Summary Statistics

Najm¹,

Chowdhary²

2017

Handbook of Uncertainty Quantification

View full text Add to dashboard Cite

Data-free inference of the joint distribution of uncertain model parameters

Cited by 20 publications

References 30 publications

Inference Given Summary Statistics

Inference Given Summary Statistics

Estimating reaction parameters in mechanism‐enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

Inference Given Summary Statistics

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