A Hierarchical Bayesian Similarity Measure for Geotechnical Site Retrieval

Abstract

Geotechnical site retrieval refers to the quantitative identification and extraction of sites similar to a given target site from predocumented generic sites in a database. This is known as the “site recognition challenge.” Recently, the second and third authors of this paper proposed a Bayesian similarity measure between a target site and generic records in the database. However, the proposed method can only retrieve “similar database records” but not “similar database sites”; that is, records are not grouped according to their test locations within a site boundary. The purpose of the current paper was to propose a novel Bayesian similarity measure between the target site and a database site to extract similar sites from a database. This “site retrieval” approach is more “explainable” to a geotechnical engineer because an engineer has an opportunity to accept or reject the identified “similar” sites based on his or her experiences and judgment. The human engineer can engage an explainable algorithm in a decision loop in a more meaningful way. Based on the hierarchical Bayesian model (HBM) previously developed by the second and third authors, this study further proposed a Bayesian method of measuring similarity between the target site and database sites for the purpose of geotechnical site retrieval. This hierarchical Bayesian measure elegantly reduces to the classical Kullback–Leibler divergence for complete multivariate data. The HBM was used to simultaneously model intrasite and intersite variability and construct the site-specific multivariate distribution for the database sites. Site retrieval was performed by measuring the similarity between the target and database sites in the form of a multivariate likelihood. It is shown that the proposed hierarchical Bayesian method can yield a meaningful interpretation of intersite similarity and can successfully be used for site retrieval. The proposed approach can also quantify the statistical uncertainty due to sparse (limited) and incomplete (missing) data.