Bayesian Probabilistic Approaches for Developing the Empirical Model for Debris-Flow Sediment Volume Using Limited Site Investigation Data
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 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.
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Data Availability Statement
All data in this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Project No. 52009037), Outstanding Young and middle-aged Science and Technology Innovation Team of Colleges and Universities in Hubei Province (T2022010), the Natural Science Foundation of Hubei Province of China (Project No. 2020CFB291), and the Wuhan Knowledge Innovation Special Project (No. 2022020801020268). The authors are also grateful to the anonymous reviewers for their helpful comments and advice.
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Published In
Natural Hazards Review
Volume 25 • Issue 1 • February 2024
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Dec 20, 2022
Accepted: Aug 8, 2023
Published online: Nov 16, 2023
Published in print: Feb 1, 2024
Discussion open until: Apr 16, 2024
ASCE Technical Topics:
- Algorithms
- Analysis (by type)
- Bayesian analysis
- Data analysis
- Engineering fundamentals
- Flow (fluid dynamics)
- Fluid dynamics
- Fluid mechanics
- Geotechnical engineering
- Geotechnical investigation
- Hydrologic engineering
- Mathematics
- Methodology (by type)
- Model accuracy
- Models (by type)
- Probability
- Research methods (by type)
- River engineering
- Sediment
- Site investigation
- Solids flow
- Statistical analysis (by type)
- Water and water resources
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