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Sampling
Published in A. C. Faul, A Concise Introduction to Machine Learning, 2019
Figure 3.8 shows the random walk generated by the steps of the Gibbs algorithm for the same normal distribution as in the examples in Figure 3.7. The samples generated by the Gibbs algorithm are highly correlated. To approximate independence between samples thinningthinning can be used. Another technique is blockingblocking, where not the conditional probabilities of individual components are used, but of sets of several components, which can be overlapping.
A Gaussian Process Emulator Based Approach for Bayesian Calibration of a Functional Input
Published in Technometrics, 2022
Zhaohui Li, Matthias Hwai Yong Tan
To sample from the posterior distribution of , we use a Metropolis-within-Gibbs algorithm given in Appendix C. The algorithm updates , and cyclically, where is updated by sampling from its full conditional inverse Gamma density, while ηi is updated by sampling from its full conditional density using the slice sampling method. The algorithm updates using a Metropolis-Hasting step with a random walk normal proposal distribution with covariance matrix obtained by linearizing the emulator mean (14) in the target full conditional density of .
Bayesian model and parameter calibration for braced excavations in soft clays
Published in Marine Georesources & Geotechnology, 2020
To this end, a new Bayesian approach for updating both model biases and soil parameters using the field data for wall deflection and ground surface settlement in braced excavations is presented in this article. This Bayesian approach is based on the Metropolis–Hastings algorithm (Metropolis et al. 1953; Hastings 1970) and the Gibbs algorithm (described in Geman and Geman 1984), and it is realized by hybrid Markov chain Monte Carlo simulation (Gelman et al. 1995; Givens and Hoeting 2005). To demonstrate this Bayesian approach, a case study is conducted using data from the Formosa excavation in Taiwan. Since both the model and the soil parameters are calibrated in this approach, it is expected that the predicted excavation-induced responses for the targeted excavation depth will be more accurate and less variable than the responses predicted using approaches where only the model or the soil parameters are calibrated.