Sensitivity analysis for Bayesian hierarchical models

Bayesian Analysis

Volumn 10, Issue 2, 2015, Pages 321-349

  Roos, Małgorzata ^a   Martins, Thiago G ^b   Held, Leonhard ^a   Rue, Håvard ^b  

^a UNIVERSITY OF ZURICH   (Switzerland)

^b NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

Base prior; Bayesian hierarchical models; Bayesian robustness; Calibration; Formal local sensitivity measure; Hellinger distance; Identifiability; Overparametrisation

Indexed keywords

EID: 84924871500     PISSN: 19360975     EISSN: 19316690     Source Type: Journal    
DOI: 10.1214/14-BA909     Document Type: Article

References (59)

1. Amari, S. (1990). Differential-Geometrical Methods in Statistics. 2nd Edition. Lecture Notes in Statistics, volume 28. Springer-Verlag.
2. Amari, S. and Nagaoka, H. (2000). Methods of Information Geometry. Oxford University Press.
3. Berger, J. O., Ríos Insua, D., and Ruggeri, F. (2000). "Bayesian Robustness." In Ríos Insua, D. and Ruggeri, F. (eds.), Robust Bayesian Analysis, 1-32. Springer-Verlag.
4. Besag, J., York, J., and Mollié, A. (1991). "Bayesian image restoration, with two applications in spatial statistics." Annals of the Institute of Statistical Mathematics, 43(1): 1-59.
5. Bhattacharyya, A. (1943). "On a measure of divergence between two statistical populations defined by their probability distributions." Bulletin of the Calcutta Mathematical Society, 35: 99-109.
6. Box, G. (1980). "Sampling and Bayes' inference in scientific modelling and robustness." Journal of the Royal Statistical Society, Series A, 143(4): 383-430.
7. Breslow, N. E. and Clayton, D. G. (1993). "Approximate inference in generalized linear mixed models." Journal of the American Statistical Association, 88(421): 9-25.
8. Cacuci, D. G., Ionescu-Bujor, M., and Navon, I. M. (2005). Sensitivity and Uncertainty Analysis. Volume II, Applications to Large-Scale Systems. Chapman & Hall.
9. Carlin, B. and Louis, T. (1998). Bayes and Empirical Bayes Methods for Data Analysis. Chapman & Hall/CRC.
10. Clarke, B. and Gustafson, P. (1998). "On the overall sensitivity of the posterior distribution to its inputs." Journal of Statistical Planning and Inference, 71(1-2): 137-150.
11. Cook, R. (1986). "Assessment of local influence." Journal of the Royal Statistical Society, Series B, 48(2): 133-169.
12. Dawid, A. (1977). "Further comments on some comments on a paper by Bradley Efron." The Annals of Statistics, 5(6): 1249.
13. Dawid, A. (1979). "Conditional independence in statistical theory." Journal of the Royal Statistical Society. Series B (Methodological), 41(1): 1-31.
14. Dey, D. and Birmiwal, L. (1994). "Robust Bayesian analysis using divergence measures." Statistics & Probability Letters, 20(4): 287-294.
15. Eberly, L. and Carlin, B. (2000). "Identifiability and convergence issues for Markov chain Monte Carlo fitting of spatial models." Statistics in Medicine, 19(17-18): 2279-2294.
16. Evans, M. and Moshonov, H. (2006). "Checking for prior-data conflict." Bayesian Analysis, 4(1): 893-914.
17. Fong, Y., Rue, H., and Wakefield, J. (2010). "Bayesian inference for generalized linear mixed models." Biostatistics, 11(3): 397-412.
18. Geisser, S. (1992). "Bayesian perturbation diagnostics and robustness." In Goel, P. and Iyengar, N. (eds.), Bayesian Analysis in Statistics and Econometrics, 289-301. Springer-Verlag.
19. Iyengar, N. (1993). Predictive Inference: An Introduction. Chapman & Hall, Inc.
20. Gelfand, A. and Sahu, S. (1999). "Identifiability, improper priors, and Gibbs sampling for Generalized Linear Models." Journal of the American Statistical Association, 94(445): 247-253.
21. Gelfand, A. and Smith, A. (1990). "Sampling-based approaches to calculating marginal densities." Journal of the American Statistical Association, 85(410): 398-409.
22. Gelman, A., Carlin, J., Stern, H., and Rubin, D. (2004). Bayesian Data Analysis. 2nd Edition. Chapman & Hall/CRC.
23. Gilks, W., Richardson, S., and Spiegelhalter, D. (1996). Markov Chain Monte Carlo. Chapman & Hall.
24. Goutis, C. and Robert, C. (1998). "Model choice in generalised linear models: A Bayesian approach via Kullback-Leibler projections." Biometrika, 85(1): 29-37.
25. Gustafson, P. (1996). "Local sensitivity of inferences to prior marginals." Journal of the American Statistical Association, 91(434): 774-781.
26. Gustafson, P. (2000). "Local robustness in Bayesian analysis." In Ríos Insua, D. and Ruggeri, F. (eds.), Robust Bayesian Analysis, 71-88. Springer-Verlag.
27. Gustafson, P. and Wasserman, L. (1995). "Local sensitivity diagnostics for Bayesian inference." The Annals of Statistics, 23(6): 2153-2167.
28. Ibrahim, J., Zhu, H., and Tang, N. (2011). "Bayesian local influence for survival models." Lifetime Data Analysis, 17(1): 43-70.
29. Jeffreys, H. (1961). Theory of Probability. Oxford University Press.
30. Kadane, J. (1992). "Comments to: "Bayesian perturbation diagnostics and robustness" by S. Geisser." In Goel, P. and Iyengar, N. (eds.), Bayesian Analysis in Statistics and Econometrics, 298-300. Springer-Verlag.
31. Kass, R., Tierney, L., and Kadane, J. (1989). "Approximate methods for assessing influence and sensitivity in Bayesian analysis." Biometrika, 76(4): 663-674.
32. Lavine, M. (1992). "Local predictive influence in Bayesian linear models with conjugate priors." Communications in Statistics - Simulation and Computation, 21(1): 269-283.
33. Le Cam, L. (1986). Asymptotic Methods in Statistical Decision Theory. Springer-Verlag.
34. Lesaffre, E. and Lawson, A. (2012). Bayesian Biostatistics. John Wiley & Sons.
35. Lindgren, F., Rue, H., and Lindström, J. (2011). "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic differential equation approach." Journal of the Royal Statistical Society, Series B., 73(4): 423-498.
36. Martins, T., Simpson, D., Lindgren, F., and Rue, H. (2013). "Bayesian computing with INLA: new features." Computational Statistics & Data Analysis, 67: 68-83.
37. McCulloch, R. (1989). "Local model influence." Journal of the American Statistical Association, 84(406): 473-478.
38. Millar, R. and Stewart, W. (2007). "Assessment of locally influential observations in Bayesian models." Bayesian Analysis, 2(2): 365-384.
39. Müller, U. (2012). "Measuring prior sensitivity and prior informativeness in large Bayesian models." Journal of Monetary Economics, 59(6): 581-597.
40. Narasimhan, B. (2005). "Lisp-Stat to Java to R." Journal of Statistical Software, 13(4): 1-10.
41. Oakley, J. and O'Hagan, A. (2004). "Probabilistic sensitivity analysis of complex models: a Bayesian approach." Journal of the Royal Statistical Society, Series B, 66(3): 751-769.
42. Pérez, C., Martín, J., and Rufo, M. (2006). "MCMC-based local parametric sensitivity estimation." Computational Statistics & Data Analysis, 51(2): 823-835.
43. Pettit, L. (1990). "The conditional predictive ordinate for the normal distribution." Journal of the Royal Statistical Society, Series B, 52(1): 175-184.
44. Plummer, M. (2001). "Local sensitivity in Bayesian graphical models." URL http://www-ice.iarc.fr/~martyn/papers/sensitivity.ps
45. Rao, C. (1945). "Information and the accuracy attainable in the estimation of statistical parameters." Bulletin of the Calcutta Mathematical Society, 37: 81-91.
46. Ríos Insua, D., Ruggeri, F., and Martín, J. (2000). "Bayesian Sensitivity Analysis." In Saltelli, A., Chan, K., and Scott, E. M. (eds.), Sensitivity Analysis, 225-244. John Wiley & Sons.
47. Robert, C. (1996). "Intrinsic losses." Theory and Decision, 40(2): 191-214.
48. Roos, M. and Held, L. (2011). "Sensitivity analysis in Bayesian generalized linear mixed models for binary data." Bayesian Analysis, 6(2): 259-278.
49. Rue, H., Martino, S., and Chopin, N. (2009). "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations." Journal of the Royal Statistical Society, Series B., 71(2): 319-392.
50. Ruggeri, F. (2008). "Bayesian Robustness." Forum: Robustness Analysis, In: European Working Group "Multiple Criteria Decision Aiding", 3(17).
51. Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., and Tarantola, S. (2008). Global Sensitivity Analysis. The Primer. John Wiley & Sons.
52. Saltelli, A., Tarantola, S., Campolongo, F., and Ratto, M. (2004). Sensitivity Analysis in Practice. A Guide to Assessing Scientific Models. John Wiley & Sons.
53. Sivaganesan, S. (2000). "Global and local robustness approaches: uses and limitations." In Ríos Insua, D. and Ruggeri, F. (eds.), Robust Bayesian Analysis, 89-108. Springer-Verlag.
54. Tierney, L. and Kadane, J. (1986). "Accurate approximations for posterior moments and marginal densities." Journal of the American Statistical Association, 81(393): 82-86.
55. Van der Linde, A. (2007). "Local influence on posterior distributions under multiplicative modes of perturbation." Bayesian Analysis, 2(2): 319-332.
56. Weiss, R. (1996). "An approach to Bayesian sensitivity analysis." Journal of the Royal Statistical Society, Series B., 58(4): 739-750.
57. Weiss, R. and Cook, R. (1992). "A graphical case statistic for assessing posterior influence." Biometrika, 79(1): 51-55.
58. Zhu, H., Ibrahim, J., Lee, S., and Zhang, H. (2007). "Perturbation selection and influence measures in local influence analysis." The Annals of Statistics, 35(6): 2565-2588.
59. Zhu, H., Ibrahim, J., and Tang, N. (2011). "Bayesian influence analysis: a geometric approach." Biometrika, 98(2): 307-323.