Hamiltonian Monte Carlo and Borrowing Strength in Hierarchical Inverse Problems

被引:20
作者
Nagel, Joseph B. [1 ]
Sudret, Bruno [1 ]
机构
[1] ETH, Inst Struct Engn, Chair Risk Safety & Uncertainty Quantificat, Stefano Franscini Pl 5, CH-8093 Zurich, Switzerland
关键词
Uncertainty quantification; Bayesian inversion; Hierarchical modeling; Markov chain Monte Carlo; Hamiltonian Monte Carlo;
D O I
10.1061/AJRUA6.0000847
中图分类号
TU [建筑科学];
学科分类号
0813 ;
摘要
Bayesian approaches to uncertainty quantification and information acquisition in hierarchically defined inverse problems are presented. The techniques comprise simple updating, staged estimation, and multilevel model calibration. In particular, the estimation of material properties within an ensemble of identically manufactured structural elements is considered. It is shown how inferring the characteristics of an individual specimen can be accomplished by exhausting statistical strength from tests of other ensemble members. This is useful in experimental situations where evidence is scarce or unequally distributed. Hamiltonian Monte Carlo is proposed to cope with the numerical challenges of the devised approaches. The performance of the algorithm is studied and compared to classical Markov chain Monte Carlo sampling. It turns out that Bayesian posterior computations can be drastically accelerated. (C) 2015 American Society of Civil Engineers.
引用
收藏
页数:12
相关论文
共 61 条
[1]  
[Anonymous], 2014, ARXIV14116669
[2]  
Ballesteros G. C., 2014, Vulnerability, Uncertainty, and Risk. Quantification, Mitigation, and Management. Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA). Proceedings, P1615
[3]   A review of selected techniques in inverse problem nonparametric probability distribution estimation [J].
Banks, H. Thomas ;
Kenz, Zackary R. ;
Thompson, W. Clayton .
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2012, 20 (04) :429-460
[4]   Nonlinear methods for inverse statistical problems [J].
Barbillon, Pierre ;
Celeux, Gilles ;
Grimaud, Agnes ;
Lefebvre, Yannick ;
De Rocquigny, Etienne .
COMPUTATIONAL STATISTICS & DATA ANALYSIS, 2011, 55 (01) :132-142
[5]   Bayesian system identification based on probability logic [J].
Beck, James L. .
STRUCTURAL CONTROL & HEALTH MONITORING, 2010, 17 (07) :825-847
[6]   Hierarchical Bayesian model updating for structural identification [J].
Behmanesh, Iman ;
Moaveni, Babak ;
Lombaert, Geert ;
Papadimitriou, Costas .
MECHANICAL SYSTEMS AND SIGNAL PROCESSING, 2015, 64-65 :360-376
[7]   Optimal tuning of the hybrid Monte Carlo algorithm [J].
Beskos, Alexandros ;
Pillai, Natesh ;
Roberts, Gareth ;
Sanz-Serna, Jesus-Maria ;
Stuart, Andrew .
BERNOULLI, 2013, 19 (5A) :1501-1534
[8]   Advanced MCMC methods for sampling on diffusion pathspace [J].
Beskos, Alexandros ;
Kalogeropoulos, Konstantinos ;
Pazos, Erik .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2013, 123 (04) :1415-1453
[9]  
Betancourt Michael, 2013, Geometric Science of Information. First International Conference, GSI 2013. Proceedings. LNCS 8085, P327, DOI 10.1007/978-3-642-40020-9_35
[10]  
Betancourt M., 2015, CURR TRENDS BAYESIAN, P79, DOI 10.1201/b18502-5