A Methodology for Estimating the Uncertainty in Model Parameters Applying the Robust Bayesian Inferences

Title & Authors
A Methodology for Estimating the Uncertainty in Model Parameters Applying the Robust Bayesian Inferences
Kim, Joo Yeon; Lee, Seung Hyun; Park, Tai Jin;

Abstract
Background: Any real application of Bayesian inference must acknowledge that both prior distribution and likelihood function have only been specified as more or less convenient approximations to whatever the analyzers true belief might be. If the inferences from the Bayesian analysis are to be trusted, it is important to determine that they are robust to such variations of prior and likelihood as might also be consistent with the analyzers stated beliefs. Materials and Methods: The robust Bayesian inference was applied to atmospheric dispersion assessment using Gaussian plume model. The scopes of contaminations were specified as the uncertainties of distribution type and parametric variability. The probabilistic distribution of model parameters was assumed to be contaminated as the symmetric unimodal and unimodal distributions. The distribution of the sector-averaged relative concentrations was then calculated by applying the contaminated priors to the model parameters. Results and Discussion: The sector-averaged concentrations for stability class were compared by applying the symmetric unimodal and unimodal priors, respectively, as the contaminated one based on the class of $\small{{\varepsilon}}$-contamination. Though $\small{{\varepsilon}}$ was assumed as 10%, the medians reflecting the symmetric unimodal priors were nearly approximated within 10% compared with ones reflecting the plausible ones. However, the medians reflecting the unimodal priors were approximated within 20% for a few downwind distances compared with ones reflecting the plausible ones. Conclusion: The robustness has been answered by estimating how the results of the Bayesian inferences are robust to reasonable variations of the plausible priors. From these robust inferences, it is reasonable to apply the symmetric unimodal priors for analyzing the robustness of the Bayesian inferences.
Keywords
Atmospheric dispersion;Robust Bayesian inference;$\small{{\varepsilon}}$-contamination;Uncertainty;
Language
English
Cited by
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