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The application of a Bayesian approach to assess the seismic vulnerability of historical centers
Published in Koen Van Balen, Els Verstrynge, Structural Analysis of Historical Constructions: Anamnesis, Diagnosis, Therapy, Controls, 2016
S. Taffarel, G.P. Campostrini, L. Rosato, C. Marson, F. da Porto, C. Modena
Figure 3. Prior (a) and posterior (b) normal-inverse-gamma distribution. Scatterplots representing prior and posterior normal-inverse-gamma are obtained generating 1000 samples both from the prior and the posterior by adopting the Monte Carlo method.
Bayesian learning of structures of ordered block graphical models with an application on multistage manufacturing processes
Published in IISE Transactions, 2021
Chao Wang, Xiaojin Zhu, Shiyu Zhou, Yingqing Zhou
According to the assumption A1, for a sub-graph realization we can have the following relationships among nodes: where is the coefficient vector for the parent nodes in and is the variance for Yk. Note that we use the vector to represent a sample of parent nodes in Equation (9) describes the conditional distribution of Yk given the The basic idea of the Bayesian linear model is to assign a Normal-inverse-Gamma distribution for the parameters and As a result, the will be the conjugate prior for which makes the likelihood analytically available.
Redundancy-based service life assessment of corroded reinforced concrete elements considering parameter uncertainties
Published in Structure and Infrastructure Engineering, 2018
When the variables Xi are normally distributed, it is common practice to choose a normal-inverse-gamma distribution as the joint distribution function for the variables Mi and Σi. As indicated in (Gelman, Carlin, Stern, & Rubin, 2004), the marginal distribution of the variance is scaled inverse- and the conditional distribution of the mean, given the variance, is normal. Based on this, the standard deviation of both the mean value (i.e. σMi) and standard deviation (σΣi) can be determined as:
Performance-oriented risk evaluation and maintenance for multi-asset systems: A Bayesian perspective
Published in IISE Transactions, 2022
Xiujie Zhao, Zhenglin Liang, Ajith K. Parlikad, Min Xie
In the last section, we used the posterior mean of the cost rate to optimize the maintenance policy. Bayesian analysis allows other criteria to characterize different statistics of the posterior distribution. For example, a maximum a posteriori estimator has been widely used in addition to the posterior mean (Bassett and Deride, 2019), which implies that the posterior mode can be a reasonable criterion for the problem. Following Equation (16) in Section 3.1, we can rewrite the criterion as whereand based on the property of the normal-inverse-gamma distribution, we can simply imply that