An uncertainty quantification framework for logistic regression based geospatial natural hazard modeling

Abstract

There is a class of data-driven global natural hazard predictive models that take advantage of broadly available geospatial proxies. These data-driven geospatial models have been commonly used for landslides and are becoming more available in recent years for liquefaction. Logistic regression is the most common method for predicting these ground failure occurrences. These models do not often include robust quantification of uncertainties although they are widely used in the pre-disaster planning and post-disaster response around the world. Taking the logistic regression based global geospatial liquefaction model (GGLM) (Zhu et al., 2017) as an example, we propose an uncertainty quantification (UQ) framework that consists of characterization of different sources of uncertainty, model sensitivity analysis, and forward uncertainty propagation. In this study, we have identified the main sources of uncertainty in such predictive models as parameter estimation uncertainty, modeling error, and geospatial input uncertainty. A Bayesian inference algorithm is used to quantify the posterior distribution of model parameters and quantify model parameter estimation uncertainties which are found to be negligible when a large amount of data is used in the parameter estimation process. Modeling errors are characterized based on the observed residuals between model predictions and measurements and by fitting a Gaussian distribution to the liquefaction probability residuals. The geospatial input uncertainties are characterized using the literature and expert judgment and propagated into model output. Second, we investigate the sensitivity of model output to different uncertain inputs and find that the variance of model output is largely controlled by the geospatial input uncertainties and model errors. Last, we propose an approximate forward uncertainty propagation method, which provides comparable results to a Monte Carlo simulation-based method with better computational efficiency. The proposed UQ framework provides a measure of uncertainty on model predictions and can be applied to any logistic-regression models and other geospatial modeling problems.