Statistical characterization of random field parameters using frequentist and Bayesian approaches

Abstract

Because information collected in a site investigation is limited, it is not possible to obtain actual values for the mean, standard deviation, and scale of fluctuation for a soil property of interest. The deviation between the estimated values and the actual values is called the statistical uncertainty. There are at least two schools of thought on how to model the statistical uncertainty: frequentist thought and Bayesian thought. The purpose of this paper is to discuss their philosophical difference, to show how to quantify the statistical uncertainty based on these two distinct schools of thought, and to compare their performances. To quantify the statistical uncertainty, the confidence interval will be used for the frequentist school of thought, whereas the posterior probability distribution will be used for the Bayesian school of thought. Examples will be presented to compare the performances of these two schools of thought in terms of their consistencies. The results show that, in general, the Bayesian thought performs better in terms of consistency. In particular, the Markov chain Monte Carlo method is recommended when the amount of information available is very limited.