Sign Constrained Bayesian Inference for Nonstationary Models of Extreme Events

Recent studies show that many of the extreme events in hydrology can be modeled more realistically by means of a nonstationary generalized extreme value (GEV) distribution. However, existing approaches for estimating the parameters can mistake a positive trend in the data to be negative. This can lead to underdesigning in engineering projects. To address this issue, this work devises a sign constrained Bayesian inference method for nonstationary GEV distributions. This new approach ensures that the final GEV model embodies a trend consistent with the physical understanding of the underlying phenomenon and design requirements. The advantage of using the sign constrained Bayesian approach is twofold: first, it produces a probability distribution instead of a point estimate of the model parameters; and second, it affords a natural method of uncertainty quantification, thus giving greater confidence to engineers in selecting design parameter values for civil and mechanical structures to withstand extreme events. The merit of the proposed Bayesian approach is illustrated using two water level datasets pertaining to tidal rivers in New Jersey. The results show that the new method is capable of appropriately handling datasets for which traditional methods return a positive or negative slope in the location parameters, and produces the posterior distribution of the parameters based on the observed data and not point estimates. Further, the availability of a probability distribution for the return event gives engineering designers and planners additional information and perspective on the risks involved.