Multi-source data-driven conjugate Bayesian inference of the distributions of soil shear strength parameter moments

Abstract

The distributions of soil shear strength parameter moments are crucial for slope reliability analyses. The expressions for the joint posterior distributions of the mean and variance of shear strength parameters $c$ and $\phi$ are derived based on conjugate Bayesian inference under the assumptions of normality and lognormality. To fuse prior distributions obtained from multiple data sources, the expression of the Jensen–Shannon (JS) divergence is generalized to two-dimensional cases. The generalized JS divergence can measure the similarity between the prior and posterior distributions so that it is adopted as the metric to determine the weights of different prior distributions. An illustrative example demonstrates that the posterior distribution inferred from the fused prior distribution can effectively integrate the information from each individual prior distribution. The weighting method based on the generalized JS divergence enhances the anti-interference ability of the fused prior distribution. Comparisons of the maximum a posteriori estimation results of the mean and variance reveal that the inference results based on the two distributional assumptions differ slightly, which can also be drawn from the comparison of the standard values. The illustrative example reveals that the proposed method can provide a reference for the posterior distribution inference of geotechnical parameter statistics.