Empirical Bayes Approach for Developing Hierarchical Probabilistic Predictive Models and Its Application to the Seismic Reliability Analysis of FRP-Retrofitted RC Bridges

Abstract

AbstractThis paper proposes a general formulation to develop hierarchical probabilistic predictive models for clustered data. The common clustering factor, shared among the data within a group, causes statistical dependence that needs to be accounted for in the estimation of unknown model parameters. The basic idea of the hierarchical formulation is that the unknown model parameters are endowed with distributions that depend on a set of shared underlying parameters, and this construction is recursive up to the highest level of the hierarchy. The usual improper noninformative prior distributions on variance parameters of hierarchical models can lead to nonexistent posterior distributions that may appear perfectly reasonable in numerical simulations. On the other hand, common proper noninformative prior distributions may also substantially affect posterior statistics. Instead, the empirical Bayes approach is proposed to objectively estimate the variance parameters. The Gibbs sampling algorithm is used to es...