{"title":"基于协方差的 MCMC,利用序列蒙特卡洛进行高维贝叶斯更新","authors":"","doi":"10.1016/j.probengmech.2024.103667","DOIUrl":null,"url":null,"abstract":"<div><p>Sequential Monte Carlo (SMC) is a reliable method to generate samples from the posterior parameter distribution in a Bayesian updating context. The method samples a series of distributions sequentially, which start from the prior distribution and gradually approach the posterior distribution. Sampling from the distribution sequence is performed through application of a resample-move scheme, whereby the move step is performed using a Markov Chain Monte Carlo (MCMC) algorithm. The preconditioned Crank–Nicolson (pCN) is a popular choice for the MCMC step in high dimensional Bayesian updating problems, since its performance is invariant to the dimension of the prior distribution. This paper proposes two other SMC variants that use covariance information to inform the MCMC distribution proposals and compares their performance to the one of pCN-based SMC. Particularly, a variation of the pCN algorithm that employs covariance information, and the principle component Metropolis Hastings algorithm are considered. These algorithms are combined with an intermittent and recursive updating scheme of the target distribution covariance matrix based on the current MCMC progress. We test the performance of the algorithms in three numerical examples; a two dimensional algebraic example, the estimation of the flexibility of a cantilever beam and the estimation of the hydraulic conductivity field of an aquifer. The results show that covariance-based MCMC algorithms are capable of producing smaller errors in parameter mean and variance and better estimates of the model evidence compared to the pCN approach.</p></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":null,"pages":null},"PeriodicalIF":3.0000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0266892024000894/pdfft?md5=bed64696875a3a53f78eb10e3b4d690e&pid=1-s2.0-S0266892024000894-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Covariance-based MCMC for high-dimensional Bayesian updating with Sequential Monte Carlo\",\"authors\":\"\",\"doi\":\"10.1016/j.probengmech.2024.103667\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Sequential Monte Carlo (SMC) is a reliable method to generate samples from the posterior parameter distribution in a Bayesian updating context. The method samples a series of distributions sequentially, which start from the prior distribution and gradually approach the posterior distribution. Sampling from the distribution sequence is performed through application of a resample-move scheme, whereby the move step is performed using a Markov Chain Monte Carlo (MCMC) algorithm. The preconditioned Crank–Nicolson (pCN) is a popular choice for the MCMC step in high dimensional Bayesian updating problems, since its performance is invariant to the dimension of the prior distribution. This paper proposes two other SMC variants that use covariance information to inform the MCMC distribution proposals and compares their performance to the one of pCN-based SMC. Particularly, a variation of the pCN algorithm that employs covariance information, and the principle component Metropolis Hastings algorithm are considered. These algorithms are combined with an intermittent and recursive updating scheme of the target distribution covariance matrix based on the current MCMC progress. We test the performance of the algorithms in three numerical examples; a two dimensional algebraic example, the estimation of the flexibility of a cantilever beam and the estimation of the hydraulic conductivity field of an aquifer. The results show that covariance-based MCMC algorithms are capable of producing smaller errors in parameter mean and variance and better estimates of the model evidence compared to the pCN approach.</p></div>\",\"PeriodicalId\":54583,\"journal\":{\"name\":\"Probabilistic Engineering Mechanics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0266892024000894/pdfft?md5=bed64696875a3a53f78eb10e3b4d690e&pid=1-s2.0-S0266892024000894-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probabilistic Engineering Mechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0266892024000894\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probabilistic Engineering Mechanics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0266892024000894","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
Covariance-based MCMC for high-dimensional Bayesian updating with Sequential Monte Carlo
Sequential Monte Carlo (SMC) is a reliable method to generate samples from the posterior parameter distribution in a Bayesian updating context. The method samples a series of distributions sequentially, which start from the prior distribution and gradually approach the posterior distribution. Sampling from the distribution sequence is performed through application of a resample-move scheme, whereby the move step is performed using a Markov Chain Monte Carlo (MCMC) algorithm. The preconditioned Crank–Nicolson (pCN) is a popular choice for the MCMC step in high dimensional Bayesian updating problems, since its performance is invariant to the dimension of the prior distribution. This paper proposes two other SMC variants that use covariance information to inform the MCMC distribution proposals and compares their performance to the one of pCN-based SMC. Particularly, a variation of the pCN algorithm that employs covariance information, and the principle component Metropolis Hastings algorithm are considered. These algorithms are combined with an intermittent and recursive updating scheme of the target distribution covariance matrix based on the current MCMC progress. We test the performance of the algorithms in three numerical examples; a two dimensional algebraic example, the estimation of the flexibility of a cantilever beam and the estimation of the hydraulic conductivity field of an aquifer. The results show that covariance-based MCMC algorithms are capable of producing smaller errors in parameter mean and variance and better estimates of the model evidence compared to the pCN approach.
期刊介绍:
This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.