An efficient computational approach for prior sensitivity analysis and cross-validation

Canadian Journal of Statistics

Volumn 38, Issue 1, 2010, Pages 47-64

  Bornn, Luke ^a   Doucet, Arnaud ^a   Gottardo, Raphael ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Cross validation; G prior; Markov chain monte carlo; Penalized regression; Prior sensitivity; Regularization path plot; Sequential monte carlo; Variable selection

Indexed keywords

EID: 77949901349     PISSN: 03195724     EISSN: 1708945X     Source Type: Journal    
DOI: 10.1002/cjs.10045     Document Type: Article

References (34)

1. J. H. Albert & S. Chib (1993). Bayesian analysis of binary and polytomous response data. Journal of the American Statistical Association, 88, 669-679.
2. F. Alqallaf & P. Gustafson (2001). On cross-validation of Bayesian models. Canadian Journal of Statistics, 29,333-340.
3. J. Besag, P. Green, D. Higdon & K. Mengersen (1995). Bayesian computation and stochastic systems (with discussion). Statistical Science, 10, 58-66.
4. S. Bhattacharya & J. Haslett (2007). Importancere-sampling MCMC forcross-validation in inverse problems. Bayesian Analysis, 2, 385-408.
5. N. Chopin (2002). A sequential particle filter method for static models. Biometrika, 89, 539-552.
6. N. Chopin (2004). Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference. Annals of Statistics, 32, 2385-2411.
7. G.E. Crooks (1998). Non equilibriumme asurements of free energy differences for microscopically reversible Markovian systems. Journal of Statistical Physics, 90, 1481-1487.
8. P. Del Moral (2004). "Feynman-Kac formulae: Genealogical and interacting particle systems with applications," Springer, New York.
9. P. Del Moral, A. Doucet & A. Jasra (2006). Sequential Monte Carlo samplers. Journal of the Royal Statistical Society: Series B, 68, 411-436.
10. A. Doucet, N. de Freitas & N. J. Gordon, Editors, (2001). "Sequential Monte Carlo Methods in Practice," Springer, New York.
11. A. Doucet, S. Godsill & C. Andrieu (2000). On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, 10, 197-208.
12. B. Efron, T. Hastie, I. Johnstone & R. Tibshirani (2004). Least angle regression. Annals of Statistics, 32, 407-499.
13. I. Epifani, S. MacEachern & M. Peruggia (2005). Case-deletion importance sampling estimators: Central limit theorems and related results. Technical Report No. 720, Department of Statistics, Ohio State University.
14. J. Geweke (1989). Bayesian inference in econometric models using Monte Carlo integration. Journal of the American Statistical Association, 88, 881-889.
15. W. R. Gilks & C. Berzuini (2001). Following a moving target: Monte Carlo inference for dynamic Bayesian models. Journal of the Royal Statistical Society: Series B, 63, 127-146.
16. P. Gustafson & L. Wasserman (1995). Local sensitivity diagnostics for Bayesian inference. Annals of Statistics, 23, 2153-2167.
17. P. Gustafson (1996). Local sensitivity of inferences to prior marginals. Journal of the American Statistical Association, 91, 774-781.
18. A. Jasra & A. Doucet (2008). Stability of sequential Monte Carlo samplers via the Foster-Lyapunovcondition. Statistics and Probability Letters, 78, 3062-3069.
19. A. M. Johansen & N. Whiteley (2009). A Modern perspective on auxiliary particle filters, In Proceedings of Workshop on Inference and Estimation in Probabilistic Time Series Models. Issac Newton Institute, June 2008.
20. S. Kirkpatrick, C. D. Gelatt & M. P. Vecchi (1983). Optimization by simulated annealing. Science, 220, 671-680.
21. G. Kitagawa (1996). Monte Carlo filter and smoother for Non-Gaussian, non-linear state space models. Journal of Computational and Graphical Statistics, 5, 1-25.
22. A. Lee, C. Yau, M. Giles, A. Doucet & C. Holmes (2009). On the Utility of Graphics Cards to Perform Massively Parallel Simulation of Advanced Monte Carlo Methods. arXiv:0905.2441v3.
23. J. S. Liu & R. Chen (1998). Sequential Monte Carlo methods for dynamic systems. Journal of the American Statistical Association, 93, 1032-1044.
24. J. S. Liu (2001). "Monte Carlo Strategies in Scientific Computing," 2nd ed., Springer, New York.
25. J. M. Marin & C. P. Robert (2007). Bayesian Care: a practical approach to computational Bayesian statistics. Springer-Verlag, New York.
26. G. McDonald & R. Schwing (1973). Instabilities of regression estimates relating air pollution to mortality. Technometrics, 15, 463-481.
27. R. Neal (2001). Annealed importance sampling. Statistics and Computing, 11, 125-139.
28. T. Park & G. Casella (2008). The Bayesian Lasso. Journal of the American Statistical Association, 103, 681-686.
29. M. Peruggia (1997). On the variability of case-deletion importance sampling weights in the Bayesian Linear Model. Journal of the American Statistical Association, 92, 199-207.
30. M. K. Pitt & N. Shephard (1999). Filtering via simulation: Auxiliary particle filters. Journal of the American Statistical Association, 94, 590-591.
31. T. A. Stamey, J. N. Kabalin, J. E. McNeal, I. M. Johnstone, F. Freiha, E.A. Redwine & N. Yang (1989). Prostate specific antigen in the diagnosis and treatment of adenocarcinoma of the prostate. Journal of Urology, 16, 1076-1083.
32. R. Tibshirani (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society: Series B, 58, 267-288.
33. B. Vidakovic (1998). Wavelet-Based Nonparametric Bayes Methods. In "Practical Nonparametric and Semiparametric Bayesian Statistics." D. Dey, P. Muller & D. Sinha (eds). Springer, New York, pp. 133-256.
34. A. Zellner (1986). On assessing prior distributions and Bayesian regression analysis with G-prior distributions. Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, 6, 233-243.