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| Titel |
Information Sharing Between Ground Motion Models from Different Regions via Dirichlet Process Priors |
| VerfasserIn |
M. Hermkes, N. Kuehn, C. Riggelsen, K. Vogel |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250067976
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| Zusammenfassung |
| In probabilistic seismic hazard analysis (PSHA) seismic ground motion data, induced by
earthquakes, are collected at different geographical regions. Instead of building ground
motion models, which estimates intensity parameters, e.g. peak ground acceleration or
spectral acceleration, given earthquake and site related parameters, for each region
individually, it is preferable to share information across the regions to increase the overall
prediction performance.
One of the most important methods to share information correlation between models is
Hierarchical Bayesian modeling, where parameters of the region–specific models are coupled
by a common prior. As a result of learning the parameters of the model and the
hyperparameters of the common prior jointly, the function estimation of a specific
region is affected by its own training data and by data from the other region related
through the coupled prior. Generally, the common prior is specified in a parametric
form with unknown hyperparameters. A drawback of such a prior by reason of its
modality is that the relationship between all ground motion models are treated equally,
but it is desirable that only similar models share information to permit negative
transfer.
To deal with these issues we propose a nonparametric hierarchical Bayesian
model where the common prior is drawn from a Dirichlet Process (DP). Such a
nonparametric prior has the ability to fit the model well with respect to the data without
restriction about the functional form of the prior distribution. Furthermore, the
employed DP prior induces a partition of region–specific models, so that models
within each cluster share the same parameterization. First of all, we present a linear
regression model, for which the weights of the covariates and the model variance are
drawn from a DP prior. As base distribution for the DP we have chosen a normal
inverse–Gamma prior which is the natural conjugate prior to the normal likelihood
of the applied regression model. In addition, we extend this model by replacing
the linear regression model by Gaussian Processes. The resulting models can be
seen as a DP Mixture (DPM) of linear regression functions, respectively DPM of
Gaussian Processes. By choosing conjugate priors, the base distribution can be
analytically marginalized, but the sum over all latent partitions makes exact Bayesian
inference intractable. Instead of using MCMC sampling machinery which may
be slow to convergence, we apply the Bayesian Hierarchical Clustering (BHC)
algorithm (Heller and Ghahramani, Proceedings of ICML’05) to make approximative
inference.
The experiments are performed on the Next Generation Attenuation (NGA) and Allen &
Wald data set. For comparison we also consider the performance of a single task
learning method (training a separate model for each task) and a complete pooling
approach (train a model on the complete data) as baseline methods. The results show
improved prediction performance of the DPM models compared to these baseline
methods. |
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