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.
A Bayesian Data Analytics Approach to Buildings' Thermal Parameter Estimation
Modeling buildings' heat dynamics is a complex process which depends on various factors including weather, building thermal capacity, insulation preservation, and residents' behavior. Gray-box models offer an explanation of those dynamics, as expressed in a few parameters specific to built environments that can provide compelling insights into the characteristics of building artifacts. In this paper, we present a systematic study of Bayesian approaches to modeling buildings' parameters, and hence their thermal characteristics. We build a Bayesian state-space model that can adapt and incorporate buildings' thermal equations and postulate a generalized solution that can easily adapt prior knowledge regarding the parameters. We then show that a faster approximate approach using Variational Inference for parameter estimation can posit similar parameters' quantification as that of a more time-consuming Markov Chain Monte Carlo (MCMC) approach. We perform extensive evaluations on two datasets to understand the generative process and attest that the Bayesian approach is more interpretable. We further study the effects of prior selection on the model parameters and transfer learning, where we learn parameters from one season and reuse them to fit the model in other seasons. We perform extensive evaluations on controlled and real data traces to enumerate buildings' parameters within a 95% credible interval.
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- Award ID(s):
- 1544687
- NSF-PAR ID:
- 10113138
- Date Published:
- Journal Name:
- ACM e-Energy '19 Proceedings of the Tenth ACM International Conference on Future Energy Systems
- Page Range / eLocation ID:
- 89 to 99
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract We develop a prior probability model for temporal Poisson process intensities through structured mixtures of Erlang densities with common scale parameter, mixing on the integer shape parameters. The mixture weights are constructed through increments of a cumulative intensity function which is modeled nonparametrically with a gamma process prior. Such model specification provides a novel extension of Erlang mixtures for density estimation to the intensity estimation setting. The prior model structure supports general shapes for the point process intensity function, and it also enables effective handling of the Poisson process likelihood normalizing term resulting in efficient posterior simulation. The Erlang mixture modeling approach is further elaborated to develop an inference method for spatial Poisson processes. The methodology is examined relative to existing Bayesian nonparametric modeling approaches, including empirical comparison with Gaussian process prior based models, and is illustrated with synthetic and real data examples.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3307772.3328316
