Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems
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 th...
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| Autor*in: |
Lu, Fei [verfasserIn] |
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Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Journal of computational physics - Amsterdam : Elsevier, 1966, 282(2015), Seite 138-147 |
|---|---|
| Übergeordnetes Werk: |
volume:282 ; year:2015 ; pages:138-147 |
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| DOI / URN: |
10.1016/j.jcp.2014.11.010 |
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10.1016/j.jcp.2014.11.010 doi PQ20160617 (DE-627)OLC1964692202 (DE-599)GBVOLC1964692202 (PRQ)a1680-59edea7579bb04b5ebb9db8e89cab032feded125f3ebca29efad04b56773cc20 (KEY)0034221120150000282000000138limitationsofpolynomialchaosexpansionsinthebayesia DE-627 ger DE-627 rakwb eng 530 510 000 DNB Lu, Fei verfasserin aut Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier 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. Numerical Analysis Computation Statistics Mathematics Morzfeld, Matthias oth Tu, Xuemin oth Chorin, Alexandre J oth Enthalten in Journal of computational physics Amsterdam : Elsevier, 1966 282(2015), Seite 138-147 (DE-627)129359084 (DE-600)160508-2 (DE-576)014731401 0021-9991 nnns volume:282 year:2015 pages:138-147 http://dx.doi.org/10.1016/j.jcp.2014.11.010 Volltext http://arxiv.org/abs/1404.7188 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_21 GBV_ILN_70 AR 282 2015 138-147 |
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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. |
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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. |
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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. |
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