A Bayesian model for truncated regression for the estimation of empirical ground-motion models

We present a Bayesian model for the estimation of ground-motion models that allows one to account for truncated data. Truncated data occurs in ground-motion model development because instruments do not record continuously, but only when triggered. The model is formulated as a multi-level model and incorporates event and station terms. The model considers truncation on one variable [e.g., peak ground acceleration (PGA)], and models the joint occurrence of PGA and other ground-motion intensity measures, while conditioning on the truncation for PGA. Initially, we perform numerical experiments on simulated data sets and show that not taking data truncation into account leads to biased models. Regressions using the proposed truncated model can recapture the functions used in the simulation well, and perform comparable to alternative approaches used in the past. Subsequently, we show the impact of the truncated model on observed ground-motion data representing moderate and high trigger levels, 2–4 gal and 10 gal, respectively. Differences to a model that does not take truncation into account occur at larger distances, and are more severe for the high trigger level data. For untruncated regression, the values of the standard deviations are underestimated.