ABSTRACT One of the main concerns in structural reliability is the calculation of very small failure probabilities, such as events expected to occur once in 10,000 years. A major difficulty in this is that the actions, which structures should withstand, are inferred from 50-100 years of observations. Hence, probabilistic models of actions are affected by substantial uncer- tainty, which might dominate the reliability (Coles & Pericchi 2003). These uncertainties are referred to as statistical uncertainties and the current practice in civil engineering typically neglects them. The aim of this paper is to explore the effect of this omission and to critically compare the available statistical ap- proaches to incorporate statistical uncertainty into probabilistic models. Ground snow load observations are selected for the quantitative comparison and the results for three locations from the Carpathian region are presented in details. Four different distribution functions are studied: two-parameter (LN2), three-parameter lognormal (LN3), Gumbel, and generalised extreme value distributions (GEV). Frequentist and Bayesian approaches are considered to parameter estimation, uncertainty quantification, and model averaging. SWE [mm] GEV 0 50 100 150 200 Gumbel Return period [year] SWE [mm] LN3 1.1 10 100 1000 0 50 100 150 200 Return period [year] LN2 1.1 10 100 1000 Figure 1: Location 2, maximum likelihood fitted distributions with 90% confidence intervals in Gumbel space. The numerical results indicate that for small to medium sample sizes the effect of statistical uncer- tainties can be substantial (Figure 1) and should be accounted for in reliability studies. For three- parameter distributions the models without statistical uncertainty may underestimate the 1000-year return period fractiles by 20% compared to the models which incorporate this uncertainty. This corresponds to about 0.5-times smaller return period for the same fractile. Numerical analysis of the annual maxima of ground snow loads reveals that the Gumbel distribu- tion provides unrealistically narrow uncertainty in- tervals (Figure 1). Use of the generalised extreme value distribution is thus recommended. The study indicates that unlike the frequentist statistics, the Bayesian paradigm offers a coherent and rational way to incorporate statistical uncertainties. It is ar- gued that the posterior predictive distribution should be applied in reliability studies. The results indicate that an applied distribution type has a larger effect on representative fractiles than the parameter estima- tion uncertainty. Since sample sizes are typically small, physical models are unavailable, and statisti- cal criteria fail to provide unambiguous results con- cerning appropriate probabilistic distribution, con- sensus on distribution type needs to be reached between meteorologists and reliability experts. ACKNOWLEDGEMENT This work was partly supported by the International Visegrad Fund Intra-Visegrad Scholarship (contract no. 51401089) and by the Czech Science Foundation (project no. P105/12/G059). REFERENCES Coles, S. & Pericchi, L. 2003. Anticipating catastrophes through extreme value modelling. Journal of the Royal Sta- tistical Society. Series C (Applied Statistics) 52(4): 405- 416. Model comparison and quantification of statistical uncertainties for annual maxima of ground snow loads Á. Rózsás Budapest University of Technology and Economics, Department of Structural Engineering, Budapest, Hungary M. Sýkora Czech Technical University in Prague, Klokner Institute, Prague, Czech Republic