Robust Parameter Estimation for Snow Load Induced by Annual Maximum Snow Accumulation Using Constrained Bayesian Priors

Abstract

This paper develops a Bayesian framework to estimate the parameters of the Generalized Extreme Value (GEV) distribution for the weight induced by annual maximum accumulations of snow, referred to as the snow load, using a Hamiltonian Monte Carlo (HMC) algorithm as implemented in the \enquote{extremMHMC} R package developed alongside this paper. Key to the approach is the use of strong prior distributions for the shape parameter that are appropriate in the context of snow loads, which helps to ensure robustness in the distribution parameter estimates for annual maximum snow loads despite small sample sizes. This robustness is key to ensuring that structural reliability analyses, which rely on the GEV distribution, produce physically realistic estimates of snow loads. Information on strong prior distributions is derived from existing studies on extreme rainfall and snowfall, with the novel use of hyperbolic tangent functions to transition the prior distribution parameters between low and high snow regimes. This approach enables global applicability of the strong prior approach while maintaining physical realism. Additionally, simulation studies confirm a reduction in Root Mean Square Error (RMSE) of the shape parameter estimate compared to frequentist methods, particularly for small sample sizes. Finally, a real-world application using a data from 9715 stations further demonstrates the feasibility of the proposed Bayesian framework for large scale implementation.