Bayesian probabilistic approaches for predicting the debris-flow sediment volume using limited site investigation data

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Abstract 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 be guaranteed 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 robust method to establish the most appropriate model for predicting the debris-flow volume based on Bayesian inference. Firstly, 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 multi-dimensional issues in Bayesian inference, a multi-chain method, specifically 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 (MCMC) methods (e.g., Metropolis-Hastings algorithm). MCMC samples of model parameters are subsequently applied to calculate the evidence of a candidate model using Gaussian copula, making the DREAM(ZS) algorithm feasible in model selection problem. Results show that compared with the pre-existing empirical relationship, the proposed approaches provide a simpler and more accurate model by reasonably considering the balance between data fitting and model uncertainty.

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