A Bayesian Vine Algorithm for Geotechnical Site Characterization Using High Dimensional, Multivariate, Limited, and Missing Data

Abstract

Geotechnical site characterization using multivariate, limited (sparse), and missing (incomplete) data is an important but challenging task, particularly in high dimensions. Toward this problem, this study proposes a Bayesian vine algorithm. In the proposed algorithm, the task of Bayesian update in higher dimensions is translated into a series of lower-dimensional (usually ≤2) update tasks using conditional correlation vine. This feature of the proposed algorithm makes it scalable and computationally efficient in higher dimensions. Multiple examples using two-dimensional (2D), five-dimensional (5D), 10-dimensional (10D), 20-dimensional (20D), 50-dimensional (50D), and 100-dimensional (100D) data are shown to demonstrate the capability of the proposed algorithm. The results suggest that the proposed algorithm can be used successfully for geotechnical site characterization. Even an ultrahigh 50D joint distribution with >1,000 parameters (1,325) can be estimated in around 20 min. The proposed algorithm can handle multivariate data sets with limited and missing values and can also handle non-Gaussian multivariate joint distributions. The proposed algorithm only considers cross-correlation in the site data and doesn’t take into account spatial correlation.