^{1,a}, Dian-Qing Li

^{1,b}, Zi-Jun Cao

^{1,c}, Mi Tian

^{2}and Yi Hong

^{3}

^{1}State Key Laboratory of Water Resources and Hydropower Engineering Science, Institute of Engineering Risk and Disaster Prevention, Wuhan University, 8 Donghu South Road, Wuhan 430072, P. R. China

^{a}hejian@whu.edu.cn

^{b}dianqing@whu.edu.cn

^{c}zijuncao@whu.edu.cn

^{2}School of Civil Engineering, Architecture and Environment, Hubei University of Technology/28 Nanli Road, Wuhan, P. R. China

^{3}College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, P. R. China

Quantitative risk assessment and management of debris flows necessitates estimation of exceedance probability of quantities (e.g., the total discharge Q_{total} and the maximum impact pressure P_{max}) crucial to the hazard assessment and planning of mitigation strategies. This is a non-trivial task because various uncertainties exist in observation data of these quantities and the number of observation data is generally limited, particularly for extreme events (e.g., those with large Q_{total} and P_{max}), which are of great interest in practice. This paper proposes a Bayesian approach to develop a probabilistic model for estimating exceedance probability of debris flows based on observation data of Q_{total} and P_{max}. The probabilistic model obtained from the proposed approach provides not only the exceedance probability but also its associated uncertainty level. For illustration, the proposed approach is applied to developing the probabilistic model of Q_{total} and P_{max} for quantitative risk assessment at Jiangjia Ravine, China. Results show that ignoring the statistical uncertainty in the exceedance probability estimated from a limited number of observation data leads to unconservative results of risk assessment.