Efficient Bayesian method for characterizing multiple soil parameters using parametric bootstrap

Abstract

This study proposes an efficient Bayesian method using parametric bootstrap in place of the inefficient conventional Bayesian method for characterizing the multivariate PDF of multiple soil parameters. The improvement of the efficiency is achieved by replacing the complex multi-dimensional integral in the conventional Bayesian method with a simple arithmetic average in the proposed method. The good efficiency of the proposed method makes it possible to characterize the multivariate PDF of multiple soil parameters using their limited multivariate site-specific test data and prior knowledge on the site. Moreover, the proposed method has no limitation on the multivariate distribution model and prior distribution of multiple soil parameters. It does not require that the multivariate distribution model is a multivariate normal distribution and the prior distribution is conjugate to the multivariate normal distribution. Two practical examples using real multivariate site-specific test data of multiple soil parameters and one numerical example with known multivariate distribution are presented to illustrate and demonstrate the proposed method. The results indicate that the proposed method performs well in characterizing the multivariate PDF of multiple soil parameters. The role of informative prior knowledge is that it can produce more accurate results than non-informative prior knowledge and thus reduce the demand for the multivariate site-specific test data of multiple soil parameters.