Hierarchical Bayesian approaches to statistical modelling of geotechnical data
Nezam Bozorgzadeh, Richard J. Bathurst
Abstract
Geotechnical data used for reliability-based design (RBD) and load and resistance factor design (LRFD) calibration can be parsed into subgroups based on material type, location, test method, and so on. Most often statistical analyses assume all data fall within a representative envelope, and pool (combine) all data into a single large data set without rigorously evaluating the veracity of this assumption. Adopting a Bayesian view, we introduce hierarchical/multilevel models as the more suitable alternative that takes into account multiple variation sources. Rather than assuming an identical parameter for data in all groups, hierarchical models assume exchangeable group-specific parameters, or informally, “similar but not identical” parameters. The utility of Bayesian hierarchical modelling is demonstrated by examining the accuracy of three reinforcement load models for polyester strap mechanically stabilised earth (MSE) walls and a simple hierarchical model as an example. We show that hierarchical models (i) have the customary complete pooling approach as their limiting case, (ii) quantify uncertainty from different sources of variation, (iii) prevent under-fitting, and (iv) can be used as tools for understanding the variations in the data. A simple RBD/LRFD example shows practical implications of hierarchical modelling of bias data. Finally, more complex/flexible hierarchical models are briefly discussed.Abbreviations: AASHTO: American Association of State Highway and Transportation Officials; ANOVA: analysis of variance; CDF: cumulative distribution function; CI: credible interval; COV coefficient of variation; DIC: deviance information criterion; LOGOIC: leave-one-group-out information criteria; LOOIC: leave-one-out information criteria; LM: load model; lppd: log pointwise predictive density; LRFD: load and resistance factor design; MCMC: Markov chain Monte Carlo; MSE: mechanically stabilised earth (wall); NHT: null hypothesis testing; PET: polyester; PGM: probabilistic graphical model; RBD: reliability-based design; WAIC: Watanabe-Akaike information criterion.