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Fast matrix algebra for Bayesian model calibration
In Bayesian model calibration, evaluation of the likelihood function usually involves finding the inverse and determinant of a covariance matrix. When Markov Chain Monte Carlo (MCMC) methods are used to sample from the posterior, hundreds of thousands of likelihood evaluations may be required. In th...
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| Published in: | Journal of statistical computation and simulation 2021-05, Vol.91 (7), p.1331-1341 |
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| Main Authors: | , |
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| cites | cdi_FETCH-LOGICAL-c385t-3e6dc623ab1c24f618a3e703667e563c4d875e20a8b5d12507df925430a783833 |
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| container_title | Journal of statistical computation and simulation |
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| creator | Rumsey, Kellin N. Huerta, Gabriel |
| description | In Bayesian model calibration, evaluation of the likelihood function usually involves finding the inverse and determinant of a covariance matrix. When Markov Chain Monte Carlo (MCMC) methods are used to sample from the posterior, hundreds of thousands of likelihood evaluations may be required. In this paper, we demonstrate that the structure of the covariance matrix can be exploited, leading to substantial time savings in practice. We also derive two simple equations for approximating the inverse of the covariance matrix in this setting, which can be computed in near-quadratic time. The practical implications of these strategies are demonstrated using a simple numerical case study and the
"quack"
R
package. For a covariance matrix with 1000 rows, application of these strategies for a million likelihood evaluations leads to a speedup of roughly 4000 compared to the naive implementation |
| doi_str_mv | 10.1080/00949655.2020.1850729 |
| format | article |
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| ispartof | Journal of statistical computation and simulation, 2021-05, Vol.91 (7), p.1331-1341 |
| issn | 0094-9655 1563-5163 |
| language | eng |
| recordid | cdi_proquest_journals_2519159153 |
| source | Taylor and Francis Science and Technology Collection |
| subjects | 41-04 62-04 Bayesian analysis Bayesian model calibration Calibration Covariance matrix determinant fast inverse likelihood Markov chains Mathematical analysis Matrix algebra Monte Carlo simulation |
| title | Fast matrix algebra for Bayesian model calibration |
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