Constructing Quasi-Site-Specific Multivariate Probability Distribution Using Hierarchical Bayesian Model

In geotechnical engineering, it is challenging to construct a site-specific multivariate probability distribution model for soil/rock properties because the site-specific data are usually sparse and incomplete. In contrast, there are abundant generic soil/rock data in the literature for the construction of a generic multivariate probability distribution model, but this model is typically biased and/or imprecise for a specific site. A hybridization method has been proposed to combine these two sources of soil/rock data (site-specific data and a generic database) to produce a quasi-site-specific model, but this method is essentially heuristic. In the current paper, a more rational method that exploits the geologic origin of soil/rock data is proposed. There is a tendency for data to be more similar within a single site and less similar between sites. This is called site uniqueness in geotechnical engineering practice, but no data-driven methods exist to quantify this data feature currently. The hierarchical Bayesian model (HBM) is a natural model to exploit this group information. The grouping criterion can be site localization, soil/rock types, or others. This paper only studies the group criterion based on site localization. This means that a generic database is now viewed as a collection of data groups labeled by qualitative site labels. This site label does not contain any quantitative information such as GPS location, it merely demarcates each group as distinct. The novel contribution is the development of an efficient HBM with closed-form conditional probabilities based on suitably chosen conjugate priors that can handle multivariate, uncertain and unique, sparse, incomplete, and potentially corrupted (MUSIC) data containing site labels. Numerical comparisons between the hybridization method (which cannot incorporate group information) and HBM show that even the simple qualitative knowledge that data belong to a geographically constrained site can improve the estimation of soil/rock properties. The GPS location of each site is not needed.