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Bayesian parameter estimation of duration-based variables used in post-earthquake building recovery modeling

A Bayesian parameter estimation methodology for updating the distributions of the duration-based variables used in post-earthquake building recovery modeling is presented. The distributions of the recovery-related parameters specified in the resilience-based earthquake design initiative (REDi) and HAZUS are used as the basis of the priors. A data set of observed building damage and recovery following the 2014 South Napa earthquake is assembled and used to illustrate the proposed methodology. The recovery data set includes the permit acquisition and repair time for over 800 buildings affected by the earthquake. With this data, the conjugate prior (CP) and Markov Chain Monte Carlo (MCMC) methods are implemented to update the probability distribution parameters for the duration-based recovery variables. While the CP approach is easier to implement because it offers an analytical solution, the MCMC provides more flexibility in terms of the types of prior and sampling distributions that can be accommodated. Moreover, the results from a comparative implementation on the Napa data set shows that the MCMC method provides a reasonable approximation of the posterior marginal distribution of the duration-based recovery variables relative to the CP analytical solution.