Approximating probability densities by iterated Laplace approximations

Journal of Computational and Graphical Statistics

Volumn 20, Issue 3, 2011, Pages 656-669

  Bornkamp, Björn ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Bayes factor; Importance sampling; Markov chain monte carlo; Nonlinear regression; Normalization constant

Indexed keywords

EID: 80053364251     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/jcgs.2011.10099     Document Type: Article

References (30)

1. Andrieu, C., and Moulines, É. (2006), "On the Ergodicity Properties of Some Adaptive MCMC Algorithms," The Annals of Applied Probability, 16, 1462-1505. [658]
2. Ardia, D., Hoogerheide, L. F., and van Dijk, H. K. (2009), "Adaptive Mixture of Student-t Distribution as a Flexible Candidate Distribution for Efficient Simulation: The R Package 'AdMit'," Journal of Statistical Software, 29, 1-32. [658]
3. Azzalini, A., and Capitanio, A. T. (2003), "Distributions Generated by Perturbation of Symmetry With Emphasis on a Multivariate Skew t Distribution," Journal of the Royal Statistical Society, Ser. B, 65, 367-389. [662]
4. Barron, A. R., Cohen, A., Dahmen, W., and DeVore, R. A. (2008), "Approximation and Learning by Greedy Algorithms," The Annals of Statistics, 36, 64-94. [657]
5. Bühlmann, P., and Yu, B. (2003), "Boosting With the L2 Loss: Regression and Classification," Journal of the American Statistical Association, 98, 324-339. [657]
6. Cappé, O., Douc, R., Guillin, A., Marin, J.-M., and Robert, C. P. (2008), "Adaptive Importance Sampling in General Mixture Classes," Statistics and Computing, 18, 447-459. [658,664]
7. DiCiccio, T. J., Kass, R. E., Raftery, A., and Wasserman, L. (1997), "Computing Bayes Factors by Combining Simulation and Asymptotic Approximations," Journal of the American Statistical Association, 92, 903-915. [657]
8. Dutang, C. (2009), randtoolbox: Generating and Testing Random Numbers, R package version 1.07. [660]
9. Evans, M., and Swartz, T. (2000), Approximating Integrals via Monte Carlo and Deterministic Methods, Oxford: Oxford University Press. [657]
10. Finley, A. O., Banerjee, S., and Carlin, B. P. (2010), spBayes: Univariate and Multivariate Spatial Modeling, R package version 0.1-8. [665]
11. Flegal, J., Haran, M., and Jones, G. (2008), "Markov Chain Monte Carlo: Can We Trust the Third Significant Figure," Statistical Science, 23, 250-260. [667]
12. Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2003), Bayesian Data Analysis (2nd ed.), Boca Raton, FL: Chapman & Hall. [657,659]
13. Geyer, C. J. (2010), mcmc: Markov Chain Monte Carlo, R package version 0.7-5. [665]
14. Gilks, W. R., Roberts, G. O., and Sahu, S. K. (1998), "Adaptive Markov Chain Monte Carlo Through Regeneration," Journal of the American Statistical Association, 93, 1045-1054. [662]
15. Giordani, P., and Kohn, R. (2010), "Adaptive Independent Metropolis-Hastings by Fast Estimation of Mixtures of Normals," Journal of Computational and Graphical Statistics, 19, 243-259. [658]
16. Goldfarb, D., and Idnani, A. (1982), "Dual and Primal-Dual Methods for Solving Strictly Convex Quadratic Programs," in Numerical Analysis, ed. J. Hennart, Berlin: Springer-Verlag, pp. 226-239. [661]
17. Haran, M., and Tierney, L. (2010), "On Automating Markov Chain Monte Carlo for a Class of Spatial Models," technical report, Dept. of Statistics, Pennsylvania State University, USA. [657]
18. Hartigan, J. A., and Wong, M. A. (1979), "A k-Means Clustering Algorithm," Applied Statistics, 28, 100-108. [661]
19. Kong, A., Liu, J. S., and Wong, W. H. (1994), "Sequential Imputation and Bayesian Missing Data Problems," Journal of the American Statistical Association, 89, 278-288. [663]
20. Minka, T. (2001), "Expectation Propagation for Approximate Bayesian Inference," in UAI'01: Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence, eds. J. S. Breese and D. Koller, San Francisco, CA: Morgan Kaufmann, pp. 362-369. [657]
21. Nott, D. J., Fielding, M., and Leonte, D. (2009), "On a Generalization of the Laplace Approximation," Statistics and Probability Letters, 79, 1397-1403. [657]
22. Nott, D. J., Kohn, R. J., and Fielding, M. (2008), "Approximating the Marginal Likelihood Using Copula," available at http://arxiv.org/abs/0810.5474. [657]
23. O'Hagan, A., and Forster, J. (2004), Kendall's Advanced Theory of Statistics, Volume 2B: Bayesian Inference (2nd ed.), London: Arnold. [657]
24. R Development Core Team (2010), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing. ISBN 3-900051-07-0. [661]
25. Robert, C. P., and Casella, G. (2004), Monte Carlo Statistical Methods (2nd ed.), New York: Springer. [665]
26. Roberts, G. O., and Rosenthal, J. S. (2009), "Examples of Adaptive MCMC," Journal of Computational and Graphical Statistics, 18, 349-367. [665]
27. 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, Ser. B, 71,319-392. [657]
28. Tierney, L. (1994), "Markov Chains for Exploring Posterior Distributions," The Annals of Statistics, 22, 1701-1762. [658,667]
29. Tierney, L., and Kadane, J. (1986), "Accurate Approximations for Posterior Moments and Marginal Densities," Journal of the American Statistical Association, 81, 82-86. [657]
30. Wraith, D., Kilbinger, M., Benabed, K., Cappé, O., Cardoso, J.-F., Fort, G., Prunet, S., and Robert, C. P. (2009), "Estimation of Cosmological Parameters Using Adaptive Importance Sampling," Physical Review D, 80, 023507. [662,663]