Uncertainly analyses of a process model when vague parameters are estimated with entropy and Bayesian methods

Abstract

When parameterizing a process model, it is best to use real data based on laboratory and field experimentation to directly estimate the parameters. However, this is not always possible for many practical reasons. When “vague” parameter estimates are used in a process model, they should not be treated as though they were exact and without uncertainty. Vague parameters have uncertainty, and the uncertainty can be very large. This uncertainty should be explicitly accounted for. Traditional statistical techniques can not be used to estimate vague parameters. Presented here are some results of a study where the Maximum-Entropy Principle and the Bayesian method with weighted bootstrap sampling were used to estimate unobservable parameters of a pipe model calibrated for red pine (Pinus resinosa Ait.). An uncertainty analysis based on the estimated parameters was conducted. Three parameters of this model have been estimated to demonstrate the estimation methods and uncertainty analysis with varying amounts of information. The mean values of the estimated posterior distributions based on the two methods applied in this study were very close to those of their corresponding prior distributions. The Bayesian method provided distributions that were more concentrated than their priors. This study revealed that vague parameters lead to uncertainty and the resulting uncertainty can be decreased with the methods used in this paper. The reduction in uncertainty depends on the type and amount of information available.