A methodology for sensitivity analysis in inverse problems - Application to a palaeoclimate study

Environmetrics

Volumn 18, Issue 6, 2007, Pages 647-660

  Bhattacharya, Sourabh ^a  

^a INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

Climate variable; Importance weights; Poisson regression; Reweigh; Saturated posterior; Temporal smoothness

Indexed keywords

CLIMATE VARIATION; FOSSIL RECORD; PALEOCLIMATE; POISSON RATIO; SENSITIVITY ANALYSIS;

EID: 34548460628     PISSN: 11804009     EISSN: 1099095X     Source Type: Journal    
DOI: 10.1002/env.845     Document Type: Article

References (22)

1. Athreya KB, Doss H, Sethuraman J. 1996. On the convergence of the Markov chain simulation method. The Annals of Statistics 24(1): 69-100.
2. Berger JO. 1985. Statistical Decision Theory and Bayesian Analysis. Springer-Verlag: New York.
3. Berger JO, Liseo B, Wolpert RL. 1999. Integrated likelihood methods for eliminating nuisance parameters (with discussion). Statistical Science 14(1): 1-28.
4. Bhattacharya S. 2004. Importance Resampling MCMC: A Methodology for Cross-Validation in Inverse Problems and Its Applications in Model Assessment. Doctoral thesis, Department of Statistics, Trinity College Dublin. Available at http://www.tcd.ie/Statistics/JHpersonal/thesis.pdf
5. Bhattacharya S. 2006. A Bayesian semiparametric model for organism based environmental reconstruction. Environmetrics 17(7): 763-776.
6. Bhattacharya S, Haslett J. 2004. Fast Cross Validation of a Palaeoclimate Model using IRMCMC. Technical report, Trinity College, Dublin, Ireland. Available at http://www.tcd.ie/Statistics/JHpersonal/research.htm
7. Bhattacharya S, Haslett J. 2007. Importance re-sampling MCMC for cross-validation in inverse problems. Bayesian Analysis. To appear.
8. Cornford D, Csató L, Evans DJ, Opper M. 2004. Bayesian analysis of the scatterometer wind retrieval inverse problem: some new approaches (with discussion). Journal of the Royal Statistical Society Series B 66(3): 609-626.
9. Dey D, Maiti T. 2002. Dirichlet multinomial distribution. In Encyclopedia of Environmetrics. El-Shaarawi A and Piegorsch W (eds). Fisher: Stuttgart. Wiley; 522-523.
10. Doss H. 1994. Discussion: Markov chains for exploring posterior distributions. Annals of Statistics 22(4): 1728-1734.
11. Gelfand AE, Dey DK, Chang H. 1992. Model determination using predictive distributions with implementation via sampling-based methods (with discussion). In Bayesian Statistics, vol. 4 Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds). Oxford University Press: Oxford; 147-167.
12. Gelman A, Carlin JB, Stern HS, Rubin DR. 2004. Bayesian Data Analysis, (2nd edn). Chapman and Hall: Boca Raton.
13. Haario H, Laine M, Lehtinen M, Saksman E, Tamminen J. 2004. Markov chain Monte Carlo methods for high dimensional inversion in remote sensing (with discussion). Journal of the Royal Statistical Society Series B 66(3): 591-607.
14. Haslett J, Whiley M, Bhattacharya S, Salter-Townshend M, Wilson SP, Allen JRM, Huntley B, Mitchell FJG. 2006. Bayesian palaeoclimate reconstruction (with discussion). Journal of the Royal Statistical Society Series A 169(3): 395-438.
15. Newton MA, Raftery AE. 1994. Approximate Bayesian inference with the weighted likelihood bootstrap (with discussion). Journal of the Royal Statistical Society Series B 56(1): 3-48.
16. O'Hagan A, Forster J. 2004. Kendall's Advanced Theory of Statistics, Bayesian Inference (Vol. 2B). Arnold: London.
17. Rubin D. 1988. Using the SIR algorithm to simulate posterior distributions. In Bayesian Statistics, vol. 3 Bernardo JM, DeGroot MH, Lindley DV, Smith AFM (eds). Oxford: New York; 395-402.
18. Skare Ø, Bølviken E, Holden L. 2003. Improved sampling-importance resampling and reduced bias importance sampling. Scandivanian Journal of Statistics 30: 719-737.
19. Stern HS, Cressie N. 2000. Posterior predictive model checks for disease mapping models. Statistics in Medicine 19: 2377-2397.
20. 18O climate record of the past 16,500 years and the role of the sun, ocean, and volcanoes. Quaternary Research 44: 341-354.
21. Tierney L. 1994. Markov Chains for exploring posterior distributions (with discussion). Annals of Statistics 22(4): 1701-1702.
22. Vasko K, Toivonen HT, Korhola A. 2000. A Bayesian multinomial Gaussian response model for organism based environmental reconstruction. Journal of Paleolimnology 24: 243-250.