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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. [ABSTRACT FROM AUTHOR]

Constructing a multivariate distribution model for rainfall characteristics is an important task for risk-based hydrologic design. However, most stochastic rainfall models are limited to bivariate frequentist distribution and cannot be easily generalized to multivariate (≥ 3) Bayesian settings. Towards this problem, this study presents a Bayesian vine algorithm. The presented algorithm translates the high-dimensional Bayesian update task into multiple lower-dimensional update tasks using the vine approach. The algorithm also computes the evidence, allowing Bayesian model selection of marginals and copulas in the joint distribution. Two numerical examples, a synthetic rainfall data from Canada, and a real rainfall data from China are utilized to demonstrate the algorithm's capability. The results suggest that the algorithm can satisfactorily identify and characterize the underlying marginal and dependence for the rainfall characteristics. Since the high-dimensional Bayesian update task is translated into lower-dimensional Bayesian updates, the algorithm is scalable, stable, and computationally efficient in higher dimensions. A 20-year continuous hourly rainfall record can be characterized for its depth, duration, and intensity in around 60 s without any convergence or tuning issues. Overall, this study provides a powerful Bayesian tool for constructing stochastic rainfall models, which in turn can be used in multiple civil engineering disciplines concerned with rainfall interaction. This study does not consider temporal/serial dependence but only the cross-dependence among the rainfall characteristics. • A Bayesian vine algorithm is presented for stochastic rainfall models. • The algorithm is tune-free and also allows Bayesian model selection. • Synthetic and real rainfall data are utilized to demonstrate the capability. • For further applications, MATLAB codes are provided. [ABSTRACT FROM AUTHOR]

Geotechnical site clustering refers to identifying (or learning) groups in a site-labelled soil/rock database based on inter-site similarity. It is common to cluster sites in a "region" in practice, be it a geographical area or a geologic zone. Data-driven clustering may produce solutions outside these conventional geographical/geologic demarcations. Hence, it is termed "quasi-regional" clustering. This study presents a spectral algorithm for quasi-regional clustering based on a recently proposed hierarchical Bayesian site similarity measure (HBSSM). The HBSSM is utilized to construct the inter-site similarity matrix of the site-labelled database. Quasi-regional clustering is thereafter performed based on the eigenvectors of a transformed similarity matrix. Using numerical and real examples, it is shown that the presented clustering algorithm can produce reasonable clustering results. The proposed clustering algorithm is applicable to geotechnical sites with Multivariate, Uncertain and Unique, Sparse and InComplete (MUSIC) data. It only considers similarity in means, variances, and cross-correlations. The similarity in the spatial variation (e.g., with respect to depth) is not considered. [ABSTRACT FROM AUTHOR]