Validation of nonlinear inverse algorithms with Markov chain Monte Carlo method

Journal of Geophysical Research D: Atmospheres

Volumn 109, Issue 19, 2004, Pages

  Tamminen, J ^a  

^a Finnish Metorological Institute   (Finland)

Author keywords

Atmospheric remote sensing; GOMOS; Modeling error; Nonlinear Problems; Prior information; Statistical inverse problems

Indexed keywords

DATA PROCESSING; MONTE CARLO ANALYSIS; NONLINEARITY; REMOTE SENSING;

EID: 10644233101     PISSN: 01480227     EISSN: None     Source Type: Journal    
DOI: 10.1029/2004JD004927     Document Type: Review

References (30)

1. Bertaux, J. L., G. Megie, T. Widemann, E. Chassefiere, R. Pellinen, E. Kyrölä, S. Korpela, and P. Simon (1991), Monitoring of ozone trend by stellar occultations: The GOMOS instrument, Adv. Space Res., 11 237-242.
2. Box, G. E. P., and G. C. Tiao (1992), Bayesian Inference in Statistical Analysis, John Wiley, Hoboken, N. J.
3. 3 in the 231-794 nm range, J. Quant. Spectrosc. Radiat. Transfer, 61, 509-517.
4. Chen, M.-H., Q.-M. Shao, and J. G. Ibrahim (2000), Monte Carlo Methods in Bayesian Computation, Springer-Verlag, New York.
5. Gelman, A., J. B. Carlin, H. S. Stem, and D. B. Rubin (1995), Bayesian Data Analysis, Chapman and Hall, New York.
6. Gelman, A. G., G. O. Roberts, and W. R. Gilks (1996), Efficient Metropolis jumping rules, in Bayesian Statistics V, edited by J. M. Bernardo et al., pp. 599-608, Oxford Univ. Press, New York.
7. Geman, S., and D. Geman (1984), Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE Trans. Pattern Anal. Mach. Intell., 6, 721-741.
8. Gilks, W. R., S. Richardson, and D. J. Spiegelhalter (1996), Introducing Markov chain Monte Carlo, in Markov Chain Monte Carlo in Practice, edited by W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, pp. 1-19, Chapman and Hall, New York.
9. Green, P. J. (1995), Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrica, 82, 711-732.
10. Haario, H., E. Saksman, and J. Tamminen (1999), Adaptive proposal distribution for random walk Metropolis algorithm, Comput. Stat., 14 375-395.
11. Haario, H., E. Saksman, and J. Tamminen (2001), An adaptive Metropolis algorithm, Bernoulli, 7, 223-242.
12. Haario, H., M. Laine, M. Lehtinen, E. Saksman, and J. Tamminen (2004a), MCMC methods for high dimensional inversion in remote sensing, J. R: Star. Soc., Ser. B, 66, 591-607.
13. Haario, H., E. Saksman, and J. Tamminen (2004b), Componentwise adaptation for MCMC, Comput. Stat., in press.
14. Harris, N., R. Hudson, and C. Phillips (Eds.) (1998), SPARC/IOC/GAW: Assessment of trends in the vertical distributino of ozone, Ozone Res. Monit. Proj. Rep. 43, World Meteorol. Organ., Geneva, Switzerland.
15. Hastings, W. (1970), Monte Carlo sampling methods using Markov chains and their applications, Biometrica, 57, 97-109.
16. Kyrölä, E. (1999), GOMOS ATBD - Level 2, paper presented at ESAMS99, European Symposium on Atmospheric Measurements from Space, Eur. Space Agency, Noordwijk, Netherlands, 18 -22 Jan.
17. Kyrölä, E., E. Sihvola, Y. Kotivuori, M. Tikka, T. Tuomi, and H. Haario (1993), Inverse theory for occultation measurements: 1. Spectral inversion, J. Geophys. Res., 98; 7367-7381.
18. Kyrölä, E., J. Tamminen, L. Oikarinen, E. Sihvola, P. Verronen, and G. W. Leppelmeier (1999), LIMBO - Limb and occultation measurement simulator, paper presented at ESAMS99, European Symposium on Atmospheric Measurements from Space, Eur. Space Agency, Noordwijk, Netherlands, 18-22 Jan.
19. Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller (1953), Equations of state calculations by fast computing machine, J. Chem. Phys., 21, 1087-1091.
20. Mosegaard, K., and A. Tarantola (1995), Monte Carlo sampling of solutions to inverse problems, J. Geophys. Res., 100, 12,431-12,447.
21. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flarmery (1992), Numerical Recipes in FORTRAN, The Art of Scientific Computing Clarendon, Oxford, U. K.
22. Robert, C. P., and G. Casella (2000), Monte Carlo Statistical Methods Springer-Verlag, New York.
23. Rodgers, C. D. (2000), Inverse Methods for Atmospheric Sounding: Theory and Practice, World Sci., River Edge, N. J.
24. Rodgers, C. D., and B. J. Connor (2003), Intercomparison of remote sounding instruments, J. Geophys. Res., 108(D3), 4116, doi:10.1029/2002JD002299.
25. Sambridge, M., and K. Mosegaard (2002), Monte Carlo methods in geophysical inverse problems, Rev. Geophys,, 40(3), 1009, doi:10.1029/2000RG000089.
26. Tamminen, J., and E. Kyrölä (2001), Bayesian solution for nonlinear and non-Gaussian inverse problems by Markov chain Monte Carlo method, J. Geophys. Res., 106, 14,377-14,390.
27. Tamminen, J., E. Kyrölä, and V. Sofieva (2004), Does prior information improve measurements?, in Occultations for Probing Atmosphere and Climate - Science From the OPAC-1 Workshop, edited by G. Kirchengast, U. Foelsehe, and A. K. Steiner, pp. 87-98, Springer-Verlag, New York.
28. Tarantola, A. (1987), Inverse Problem Theory, Methods for Data Fitting and Model Parameter Estimation, Elsevier Sci., New York.
29. Tierney, L. (1994), Markov chains for exploring posterior distributions, with discussion, Ann. Stat., 22, 1701-1762.
30. Yee, J.-H., et al. (2002), Atmospheric remote sensing using a combined extinctive and refractive stellar occultation technique: 1. Overview and proof-of-concept observations, J. Geophys. Res., 107, 4213, doi:10.1029/2001JD000794.