This paper provides an overview and introduction to the development of non-ergodic ground-motion models, GMMs. It is intended for a reader who is familiar with the standard approach for developing ergodic GMMs. It starts with a brief summary of the development of ergodic GMMs and then describes different methods that are used in the development of non-ergodic GMMs with an emphasis on Gaussian process (GP) regression, as that is currently the method preferred by most researchers contributing to this special issue. Non-ergodic modeling requires the definition of locations for the source and site characterizing the systematic source and site effects; the non-ergodic domain is divided into cells for describing the systematic path effects. Modeling the cell-specific anelastic attenuation as a GP, and considerations on constraints for extrapolation of the non-ergodic GMMs are also discussed. An updated unifying notation for non-ergodic GMMs is also presented, which has been adopted by the authors of this issue.

A computationally efficient methodology for propagating the epistemic uncertainty in the median ground motion in probabilistic seismic hazard analysis is developed using the polynomial chaos (PC) approach. For this application, the epistemic uncertainty in the median ground motion for a specific scenario is assumed to be lognormally distributed and fully correlated across earthquake scenarios. In the hazard calculation, a single central ground‐motion model (GMM) is used for the median along with the epistemic standard error of the median for each scenario. A set of PC coefficients is computed for each scenario and each test ground‐motion level. The additional computation burden in computing these PC coefficients depends on the order of the approximation but is less than computing the median ground motion from one additional GMM. With the PC method, the mean and fractiles of the hazard due to the epistemic uncertainty distribution of the median ground motion are computed as a postprocess that is very fast computationally. For typical values of the standard deviation of epistemic uncertainty in the median ground motion (<0.2 natural log units), the methodology accurately estimates the epistemic uncertainty distribution of the hazard over the 1%–99% range. This full epistemic range is not well modeled with just a small number of GMM branches uses in the traditional logic‐tree approach. The PC method provides more accuracy, faster computation, and reduced memory requirements than the traditional approach. For large values of the epistemic uncertainty in the median ground motion, a higher order of the PC expansion may be needed to be included to capture the full range of the epistemic uncertainty.

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