Modelling rare or extreme events is critical in many domains, including financial risk, computer security breach, network outage, corrosion and fouling, manufacturing quality and environmental extremes such as floods, snowfalls, heat-waves, seismic hazards and meteorological-oceanographic events like extra-tropical storms, hurricanes and typhoons. Statistical modelling enables us to understand extremes and design mechanisms to prevent their occurrence and manage their impact. Extreme events are challenging to characterise as they are, by definition, rare and unusual even in a big data world. The frequency and extent of extreme events is typically driven by both primary attributes (dependent variables) and secondary attributes (independent variables or covariates). Studies have shown that improved inference can be gained from including covariate effects in predictive models but this inclusion comes at a heavy computation cost. In this paper, we present a framework for risk estimation from extreme events that are non-stationary, i.e., they are dependent on multi-dimensional covariates. The approach is illustrated by estimation of offshore structural design criteria in a storm environment non-stationary with respect to storm direction, season and geographic location. The framework allows consistent assessment of structural reliability with thorough uncertainty quantification. The model facilitates estimation of risk for any combination of covariates, which can be exploited for improved understanding and ultimately optimal marine structural design. The computational burden incurred is large, especially since thorough uncertainty quantification is incorporated, but manageable using slick algorithms for linear algebraic manipulations and high-performance computing. © 2016 IEEE.