Bayesian model comparison and selection for quantifying uncertainty in active graphite nitridation

Abstract

In this paper, two stochastic model classes corresponding to different choices of (modeling and measurement) error structure are considered and compared using Bayesian framework. A single deterministic physical model of active graphite nitridation is embedded within these stochastic model classes, where estimation of surface reaction efficiency of graphite with atomic nitrogen is of primary interest. These model classes differ in the covariance matrix structure that is used in the uncertainty model to represent uncertainties associated with the physical model and experimental measurements. First model class (M1) is based on independent normal distributions assuming error to be uncorrelated between different data points whereas the second class (M2) uses γ-exponential covariance function to correlate error in the same data quantity among different data points. For each model class, Bayesian inference is used to estimate the posterior probabilities of the physical model parameters, stochastic model parameters as well as of the candidate stochastic models. Model comparison and selection is then applied based on two measures including Bayesian evidence and Bayesian information criterion (BIC), and deviance information criterion (DIC). Both measures suggest the second stochastic model class (M2) to be selected indicating that there is a correlation between errors in the same data quantity among different data points. However, with the second model class the range of uncertainty in surface reaction efficiency is estimated to be higher, which is consistent with the large scatter seen in the reported values. © 2012 by Kenji Miki.