Hybrid samplers for III-posed inverse problems

Scandinavian Journal of Statistics

Volumn 36, Issue 4, 2009, Pages 839-853

  Herbei, Radu ^a   McKeague, Ian W ^b  

^a OHIO STATE UNIVERSITY   (United States)

^b Columbia University ^*  (United States)

Author keywords

Advection diffusion; Bayesian regularization; Geometric ergodicity; Markov chain Monte Carlo; Ocean circulation; Random scan Metropolis

Indexed keywords

EID: 70350520035     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2009.00649.x     Document Type: Article

References (18)

1. Abramovich, F. Silverman, B. W. (1998). Wavelet decomposition approaches to statistical inverse problems. Biometrika 85, 115 129.
2. Al-Mahameed, M. M. (2005). Weak discrete maximum principles. Arch. Math. 41, 167 173.
3. Andersen, K. E., Brooks, S. P. Hansen, M. B. (2001). A Bayesian approach to crack detection in electrically conducting media. Inverse Problems 17, 121 136.
4. Calvetti, D., Dash, R. K., Somersalo, E. Cabrera, M. (2006). Local regularization method applied to estimating oxygen consumption during muscle activities. Inverse Problems 22, 229 243.
5. Ciarlet, P. G. (1970). Discrete maximum principles for finite difference operators. Aequationes Math. 4, 336 352.
6. Fort, G., Moulines, E., Roberts, G. O. Rosenthal, J. S. (2003). On the geometric ergodicity of hybrid samplers. J. Appl. Probab. 40, 123 146.
7. Gandy, A. Jensen, U. (2005). On goodness-of-fit tests for Aalen's additive risk model. Scand. J. Statist. 32, 425 445. (Pubitemid 41251536)
8. Haario, H., Laine, M., Lehtinen, M., Saksman, E. Tamminen, J. (2004). Markov chain Monte Carlo methods for high dimensional inversion in remote sensing. J. R. Stat. Soc. Ser. B Statist. Methodol. 66, 591 607.
9. Hadamard, J. (1923). Lectures on Cauchy's problem in linear partial differential equations. Yale University Press, New Haven
10. Herbei, R., McKeague, I. W. Speer, K. (2008). Gyres and jets: inversion of tracer data for ocean circulation structure. J. Phys. Oceanogr. 38, 1180 1202.
11. Jarner, S. Hansen, E. (2000). Geometric ergodicity of the Metropolis algorithm. Stochastic Process. Appl. 85, 341 361.
12. Kirsch, A. (1996). An introduction to the mathematical theory of inverse problems. Springer-Verlag, New York.
13. Mair, B. A. Ruymgaart, F. H. (1996). Statistical inverse estimation in Hilbert scales. SIAM J. Appl. Math. 56, 1424 1444.
14. McKeague, I. W., Nicholls, G. K., Speer, K. G. Herbei, R. (2005). Statistical inversion of South Atlantic circulation in an abyssal neutral density layer. J. Mar. Res. 63, 683 704.
15. O'Sullivan, F. (1986). A statistical perspective on ill-posed inverse problems. Statist. Sci. 1, 502 527.
16. Poole, G. Boullion, T. (1974). A survey on M-matrices. SIAM Rev. 16, 419 427.
17. Rue, H. Held, L. (2005). Gaussian Markov random fields. Chapman and Hall, London.
18. Tierney, L. (1994). Markov chain Monte Carlo for exploring posterior distributions. Ann. Statist. 22, 1701 1728.