Bayesian Inference and Maximum Likelihood Estimation for fitting Distribution Functions of Road Traffic Load Effects

Abstract

More and more bridges reach the end of their design life. Traffic loads have changed substantially over the last few decades since the design of these bridges. To prevent unnecessary costs and material use in redesign or renovation of existing bridges, it is necessary to consider realistic, location-specific traffic loads. In this paper, bridge-specific design traffic load effects are derived from load effect simulations based on Weigh-In-Motion (WIM)-data. Two methods of statistical inference, Maximum Likelihood Estimation (MLE) and Bayesian Inference (BI), are compared for deriving design values for extreme traffic load effects, following extreme value theory. Statistical uncertainties arising in fitting parametric models are addressed for both methods, specifically uncertainty in parameters of the distribution models due to limited amount of data. It was shown that the assumptions in the MLE approach are not valid. The influence of statistical uncertainties on the computed design value are therefore underestimated in the MLE approach. BI results in higher design value estimates even though unrealistic tail shape parameter values are bounded through definition of the prior distribution. BI is therefore the preferred approach since, in contrary to MLE, it provides explicit information on statistical uncertainties through the posterior distribution function. Both methods were found to be highly sensitive to the choice of threshold value.