TY - JOUR
T1 - A Bayesian model for truncated regression for the estimation of empirical ground-motion models
AU - Kuehn, Nicolas Martin
AU - Kishida, Tadahiro
AU - AlHamaydeh, Mohammad
AU - Lavrentiadis, Grigorios
AU - Bozorgnia, Yousef
N1 - Funding Information:
We would like to thank Brian Chiou and Norman Abrahamson for helpful discussion while preparing this manuscript. A similar model to the one proposed here has been used to calculate R MAX -values for the NGA-Subduction project. We would like to thank the participants of the NGA-Subduction project for the stimulating discussions. The Stan forums (https://discourse.mc-stan.org/) have been useful, with always helpful and friendly advice. Scientific cooperation of the Building and Housing Research Center (BHRC), especially Mr. Farzanegan, is gratefully appreciated. We would like Dr. Chiun-Lin Wu and Dr. Cheyu Chang for making the Taiwanese data available to us. M. AlHamaydeh is grateful for receiving partial financial support for this research work through the Faculty Research Grant program at the American University of Sharjah (FRG20-M-E152). This paper represents the opinions of the authors and does not mean to represent the position or opinions of the American University of Sharjah. We thank Peter Stafford and an anonymous reviewer for their constructive comments which greatly helped to improve the paper.
Funding Information:
We would like to thank Brian Chiou and Norman Abrahamson for helpful discussion while preparing this manuscript. A similar model to the one proposed here has been used to calculate -values for the NGA-Subduction project. We would like to thank the participants of the NGA-Subduction project for the stimulating discussions. The Stan forums ( https://discourse.mc-stan.org/ ) have been useful, with always helpful and friendly advice. Scientific cooperation of the Building and Housing Research Center (BHRC), especially Mr. Farzanegan, is gratefully appreciated. We would like Dr. Chiun-Lin Wu and Dr. Cheyu Chang for making the Taiwanese data available to us. M. AlHamaydeh is grateful for receiving partial financial support for this research work through the Faculty Research Grant program at the American University of Sharjah (FRG20-M-E152). This paper represents the opinions of the authors and does not mean to represent the position or opinions of the American University of Sharjah. We thank Peter Stafford and an anonymous reviewer for their constructive comments which greatly helped to improve the paper.
Publisher Copyright:
© 2020, Springer Nature B.V.
PY - 2020/11/1
Y1 - 2020/11/1
N2 - 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.
AB - 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.
KW - Bayesian regression
KW - Ground-motion model
KW - Truncated data
UR - http://www.scopus.com/inward/record.url?scp=85090316111&partnerID=8YFLogxK
U2 - 10.1007/s10518-020-00943-8
DO - 10.1007/s10518-020-00943-8
M3 - Article
AN - SCOPUS:85090316111
SN - 1570-761X
VL - 18
SP - 6149
EP - 6179
JO - Bulletin of Earthquake Engineering
JF - Bulletin of Earthquake Engineering
IS - 14
ER -