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Jun 6, 2022

Erratum for “Constructing Quasi-Site-Specific Multivariate Probability Distribution Using Hierarchical Bayesian Model” by Jianye Ching, Stephen Wu, and Kok-Kwang Phoon

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Publication: Journal of Engineering Mechanics
Volume 148, Issue 8
In the published paper, there are errors in the expressions for the posterior Wishart probability density function (PDF) in Table 1 and Eqs. (17) and (25). The computer codes are correct, so the analysis results in all figures are correct.
The posterior Wishart PDF in Table 1 should be
W{Σ0;(ΨΣ01+i=1MCi1)1,Mν0+λΣ0}
The corrected Eqs. (17) and (25) are as follows:
f(Σ0|X,μ,C,μ0_,C0,ν0,a_)|Σ0|(Mν0+λΣ01)/2·e(1/2)tr[Σ0×(ΨΣ01+i=1MCi1)]=W{Σ0;(ΨΣ01+i=1MCi1)1,Mν0+λΣ0}
(17)
Σ0W{Σ0;(ΨΣ01+i=1MCi1)1,Mν0+λΣ0}
(25)
Additionally, there are errors in the expressions “/C0,kk” in Eqs. (19) and (27). The computer codes are correct, so the analysis results in all figures is correct.
The correct versions of Eqs. (19) and (27) are as follows:
f(ak|X,μ,C,Θ,a_k)ak(n+1)/2α1·e(β+2C0,kk1)/ak=IG(ak;α+n+12,β+2C0,kk1)
(19)
akIG(ak;α+n+12,β+2C0,kk1)
(27)
where C0,kk1 denotes the (k,k) entry in the C01 matrix.
To preserve the published version of record, these details have been corrected only in this erratum.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 148Issue 8August 2022

History

Received: Jan 15, 2022
Accepted: Mar 25, 2022
Published online: Jun 6, 2022
Published in print: Aug 1, 2022
Discussion open until: Nov 6, 2022

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Professor, Dept. of Civil Engineering, National Taiwan Univ., #1 Roosevelt Rd. Section 4, Taipei 10617, Taiwan (corresponding author). ORCID: https://orcid.org/0000-0001-6028-1674. Email: [email protected]
Stephen Wu, M.ASCE [email protected]
Associate Professor, Dept. of Statistical Data Science, Institute of Statistical Mathematics, Research Organization of Information and Systems, Tachikawa, Tokyo 190-8562, Japan; Graduate Univ. for Advanced Studies, Tachikawa, Tokyo 190-8562, Japan. Email: [email protected]
Kok-Kwang Phoon, F.ASCE [email protected]
Professor, Singapore Univ. of Technology and Design, 8 Somapah Rd., Singapore 487372, Singapore. Email: [email protected]

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