Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems
被引:35
作者:
Lu, Fei
论文数: 0引用数: 0
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机构:
Lawrence Berkeley Natl Lab, Berkeley, CA 94720 USA
Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USALawrence Berkeley Natl Lab, Berkeley, CA 94720 USA
Lu, Fei
[1
,2
]
Morzfeld, Matthias
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机构:
Lawrence Berkeley Natl Lab, Berkeley, CA 94720 USA
Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USALawrence Berkeley Natl Lab, Berkeley, CA 94720 USA
Morzfeld, Matthias
[1
,2
]
Tu, Xuemin
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机构:
Univ Kansas, Dept Math, Lawrence, KS 66045 USALawrence Berkeley Natl Lab, Berkeley, CA 94720 USA
Tu, Xuemin
[3
]
Chorin, Alexandre J.
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机构:
Lawrence Berkeley Natl Lab, Berkeley, CA 94720 USA
Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USALawrence Berkeley Natl Lab, Berkeley, CA 94720 USA
Chorin, Alexandre J.
[1
,2
]
机构:
[1] Lawrence Berkeley Natl Lab, Berkeley, CA 94720 USA
[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
[3] Univ Kansas, Dept Math, Lawrence, KS 66045 USA
Polynomial chaos expansion;
Bayesian inverse problem;
Monte Carlo sampling;
UNCERTAINTY QUANTIFICATION;
INFERENCE;
EQUATIONS;
D O I:
10.1016/j.jcp.2014.11.010
中图分类号:
TP39 [计算机的应用];
学科分类号:
081203 ;
0835 ;
摘要:
Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data contain significant information beyond what is assumed in the prior, the surrogate posterior can be very different from the posterior, and the resulting estimates become inaccurate. One can improve the accuracy by adaptively increasing the order of the polynomial chaos, but the cost may increase too fast for this to be cost effective compared to Monte Carlo sampling without a surrogate posterior. (C) 2014 Elsevier Inc. All rights reserved.
机构:
Univ Med & Dent New Jersey, Robert Wood Johnson Med Sch, Environm & Occupat Hlth Sci Inst, Piscataway, NJ 08854 USAUniv Med & Dent New Jersey, Robert Wood Johnson Med Sch, Environm & Occupat Hlth Sci Inst, Piscataway, NJ 08854 USA
Balakrishnan, S
Roy, A
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机构:Univ Med & Dent New Jersey, Robert Wood Johnson Med Sch, Environm & Occupat Hlth Sci Inst, Piscataway, NJ 08854 USA
Roy, A
Ierapetritou, MG
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h-index: 0
机构:Univ Med & Dent New Jersey, Robert Wood Johnson Med Sch, Environm & Occupat Hlth Sci Inst, Piscataway, NJ 08854 USA
Ierapetritou, MG
Flach, GP
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机构:Univ Med & Dent New Jersey, Robert Wood Johnson Med Sch, Environm & Occupat Hlth Sci Inst, Piscataway, NJ 08854 USA
Flach, GP
Georgopoulos, PG
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h-index: 0
机构:Univ Med & Dent New Jersey, Robert Wood Johnson Med Sch, Environm & Occupat Hlth Sci Inst, Piscataway, NJ 08854 USA
机构:
Univ Med & Dent New Jersey, Robert Wood Johnson Med Sch, Environm & Occupat Hlth Sci Inst, Piscataway, NJ 08854 USAUniv Med & Dent New Jersey, Robert Wood Johnson Med Sch, Environm & Occupat Hlth Sci Inst, Piscataway, NJ 08854 USA
Balakrishnan, S
Roy, A
论文数: 0引用数: 0
h-index: 0
机构:Univ Med & Dent New Jersey, Robert Wood Johnson Med Sch, Environm & Occupat Hlth Sci Inst, Piscataway, NJ 08854 USA
Roy, A
Ierapetritou, MG
论文数: 0引用数: 0
h-index: 0
机构:Univ Med & Dent New Jersey, Robert Wood Johnson Med Sch, Environm & Occupat Hlth Sci Inst, Piscataway, NJ 08854 USA
Ierapetritou, MG
Flach, GP
论文数: 0引用数: 0
h-index: 0
机构:Univ Med & Dent New Jersey, Robert Wood Johnson Med Sch, Environm & Occupat Hlth Sci Inst, Piscataway, NJ 08854 USA
Flach, GP
Georgopoulos, PG
论文数: 0引用数: 0
h-index: 0
机构:Univ Med & Dent New Jersey, Robert Wood Johnson Med Sch, Environm & Occupat Hlth Sci Inst, Piscataway, NJ 08854 USA