<p>The processes of run-out and deposition in debris flows are highly complex. Determining reliable input parameters for dynamic numerical models to predict debris flow run-out hazards, and accounting for uncertainties in the run-out process, are critical challenges that must be addressed. To tackle these challenges, this study proposes a Bayesian-based probabilistic back analysis approach for estimating debris flow rheological parameters and employs a probabilistic prediction method to evaluate the debris flow run-out hazards. First, the probabilistic back analysis method is applied to calibrate rheological parameter distributions and derive posterior estimates by integrating observed impact areas from historical debris flow events that occurred in the same gully with prior statistical data. Additionally, a surrogate model based on support vector machines is employed to approximate the dynamic numerical model used in this study, thereby significantly enhancing the computational efficiency of the probabilistic back analysis. Subsequently, based on the updated posterior distributions and hazard classification standards, the exceedance probability of the potential debris flow impact area for each grid cell is computed using the probability density evolution method (PDEM), and corresponding hazard zoning maps are generated. The results revealed that the updated parameters via probabilistic back analysis effectively delineate critical hazard zones for potential debris flows, with the predicted extremely high hazard zone showing remarkable spatial correspondence with the observed debris flow deposition area. Compared to the prior zoning results, the predictions based on posterior parameters demonstrate significantly reduced uncertainty. Therefore, the proposed method is demonstrated to be feasible, offering a robust tool for debris flow risk assessment and management.</p>