Bayesian Probabilistic Approaches for Developing the Empirical Model for Debris-Flow Sediment Volume Using Limited Site Investigation Data.

Many empirical relationships have been proposed to relate the sediment volume to various influencing factors. However, the accuracy of such empirical relationships generally requires a large number of observation data, which is difficult to guarantee at a specific site. Moreover, based on the limited investigation data, a complicated empirical model with more input factors may be an overfitted equation. Therefore, how to develop a reliable prediction model of debris-flow sediment volume still remains a great challenge. This paper develops a probabilistic method to establish the most appropriate empirical model for predicting the debris-flow volume based on Bayesian inference. First, the limited site investigation data are preprocessed by a series of multicollinearity analysis to select the candidate input variables. Then, a Bayesian framework is developed to select the most appropriate model among alternatives and identify its corresponding model parameters based on the site investigation data and prior knowledge. To address the multidimensional issues in Bayesian inference, a multichain method, specifically the DREAM_(ZS) algorithm, is used to obtain the posterior distribution of model parameters of a candidate model to overcome the inefficient sampling problems of single-chain Markov chain Monte Carlo methods (e.g., Metropolis–Hastings algorithm). The DREAM_(ZS) algorithm is subsequently integrated with Gaussian copula to calculate the evidence of a candidate model, making it feasible in the model selection problem. Results show that compared with the preexisting empirical relationship, the proposed approaches can provide a more accurate and simpler empirical model by reasonably considering the balance between data fitting and model uncertainty. [ABSTRACT FROM AUTHOR]