Probability Density Function and Credible Region Estimation for Multivariate Uncertain Irregular Geotechnical Data

Probability Density Function (PDF) modelling and Credible Region (CR) construction are two key issues or describing Multivariate Uncertain Irregular (MUI) characteristics of geotechnical data. There are two fundamental difficulties in this task. The first is on the joint PDF modelling of complex MUI characteristics, including modelling asymmetry and/or multimodality. The second is on the CR construction of the asymmetric and/or multimodal PDF. These issues have seldom been addressed as these problems were usually considered in the case of asymmetry and unimodality only. Aiming to resolve these two difficulties, this paper proposes BAyeSIan Copula-based Highest posterior density Regions (BASIC-HR). This framework contains Stage-PDF and Stage-CR. Stage-PDF fuses copula theory and Bayesian inference to obtain the posterior joint CDF and PDF. Stage-CR fuses the posterior PDF and the concept of highest density regions to construct the Highest posterior density Regions (HR). The HR is defined as that, given a cumulative probability, any point inside the HR should have posterior probability density at least as large as any point outside the HR. Based on this definition of the HR, CR construction can be performed for MUI geotechnical data. An example is presented to illustrate the capability of the proposed framework.

Keywords: Bayesian Inference, Copula, Credible Region, Multivariate Geotechnical Data.