A Gibbs sampling algorithm for structural modal identification under seismic excitation

2018 ◽  
Vol 47 (14) ◽  
pp. 2735-2755 ◽  
Author(s):  
Binbin Li ◽  
Armen Der Kiureghian ◽  
Siu-Kui Au
Keyword(s):  
Gibbs Sampling ◽  
Modal Identification ◽  
Seismic Excitation ◽  
Sampling Algorithm ◽  
Gibbs Sampling Algorithm

scholarly journals Gibbs Sampling for Bayesian Prediction of SARMA Processes

2019 ◽  
pp. 397-418
Author(s):  
Ayman Amin
Keyword(s):  
Gibbs Sampling ◽  
Likelihood Function ◽  
Nonlinear Least Squares ◽  
Bayesian Prediction ◽  
Model Parameters ◽  
Model Errors ◽  
Multivariate Normal ◽  
Predictive Distributions ◽  
Sampling Algorithm ◽  
Gibbs Sampling Algorithm

In this article we present a Bayesian prediction of multiplicative seasonal autoregressive moving average (SARMA) processes using the Gibbs sampling algorithm. First, we estimate the unobserved errors using the nonlinear least squares (NLS) method to approximate the likelihood function. Second, we employ conjugate priors on the model parameters and initial values and assume the model errors are normally distributed to derive the conditional posterior and predictive distributions. In particular, we show that the conditional posterior distribution of the model parameters and the variance are multivariate normal and inverse gamma respectively, and the conditional predictive distribution of the future observations is a multivariate normal. Finally, we use these closed-form conditional posterior and predictive distributions to apply the Gibbs sampling algorithm to approximate empirically the marginal posterior and predictive distributions, enabling us easily to carry out multiple-step ahead predictions. We evaluate our proposed Bayesian method using simulation study and real-world time series datasets.

scholarly journals Direct Estimation of Diagnostic Classification Model Attribute Mastery Profiles via a Collapsed Gibbs Sampling Algorithm

2020 ◽  
Author(s):  
Kazuhiro Yamaguchi ◽  
Jonathan Templin
Keyword(s):  
Gibbs Sampling ◽  
Estimation Method ◽  
Real Data ◽  
Classification Model ◽  
Diagnostic Classification ◽  
Model Parameters ◽  
Sampling Algorithm ◽  
Diagnostic Classification Models ◽  
Gibbs Sampling Algorithm ◽  
Collapsed Gibbs Sampling

This paper proposes a novel collapsed Gibbs sampling algorithm that marginalizes model parameters and directly samples latent attribute mastery patterns in diagnostic classification models. This estimation method makes it possible to avoid boundary problems in the estimation of model item parameters by eliminating the need to estimate such parameters. A simulation study showed the collapsed Gibbs sampling algorithm can accurately recover the true attribute mastery status in various conditions. In a real data analysis, the collapsed Gibbs sampling algorithm indicated good classification agreement with results from a previous study.

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