A comparative study of Monte Carlo methods for efficient evaluation of marginal likelihood

Computational Statistics and Data Analysis

Volumn 56, Issue 11, 2012, Pages 3398-3414

  Ardia, David ^a,b   Baştürk, Nalan ^c   Hoogerheide, Lennart ^c   Van Dijk, Herman K ^c  

^a UNIVERSITY OF FRIBOURG   (Switzerland)

^b Aeris CAPITAL AG   (Switzerland)

^c ERASMUS UNIVERSITY ROTTERDAM   (Netherlands)

Author keywords

Adaptive mixture of Student t distributions; Bayes factor; Bridge sampling; Importance sampling; Marginal likelihood

Indexed keywords

BAYES FACTOR; COMPARATIVE ANALYSIS; COMPARATIVE STUDIES; COMPUTATIONALLY EFFICIENT; ESTIMATION STRATEGIES; GARCH MODELS; MARGINAL LIKELIHOOD; MONTE CARLO SIMULATION METHODS; NON-LINEAR REGRESSION; POSTERIOR DISTRIBUTIONS; SIMULATION TECHNIQUE; STANDARD ERRORS; STRATEGIC CHOICE; STUDENT-T DISTRIBUTION;

IMPORTANCE SAMPLING; LINEAR REGRESSION;

MONTE CARLO METHODS;

EID: 84862009381     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2010.09.001     Document Type: Article

References (41)

1. Ardia, D.; Hoogerheide, L.F.; Van Dijk, H.K.; 2008. AdMit: adaptive mixture of Student-t distributions in R. URL: http://CRAN.R-project.org/package= AdMit.
2. D. Ardia, L.F. Hoogerheide, and H.K. Van Dijk Adaptive mixture of Student-t distributions as a flexible candidate distribution for efficient simulation: the R package AdMit Journal of Statistical Software 29 3 2009 1 32 URL: http://www.jstatsoft.org/v29/i03
3. D. Ardia, L.F. Hoogerheide, and H.K. Van Dijk AdMit: adaptive mixtures of Student-t distributions The R Journal 1 1 2009 25 30
4. Ardia, D.; Hoogerheide, L.F.; Van Dijk, H.K.; 2009c. To bridge, to warp or to wrap: a comparative study of Monte Carlo methods for efficient evaluation of marginal likelihoods. Tinbergen Institute Discussion Paper TI2009-017/4.
5. M.C. Ausín, and P. Galeano Bayesian estimation of the Gaussian mixture GARCH model Computational Statistics & Data Analysis 51 5 2007 2636 2652
6. D.M. Bates, and D.G. Watts Nonlinear Regression Analysis and its Applications 1988 Wiley New York
7. L. Bauwens, C.S. Bos, H.K. Van Dijk, and R.D. Van Oest Adaptive radial-based direction sampling: some flexible and robust Monte Carlo integration methods Journal of Econometrics 123 2 2004 201 225
8. Bauwens, L.; Rombouts, J.V.K.; 2010. On marginal likelihood computation in change-point models. Computational Statistics & Data Analysis (in print).
9. M.H. Chen, Q.M. Shao, and J.G. Ibrahim Monte Carlo Methods in Bayesian Computation 2000 Springer Verlag
10. S. Chib Marginal likelihood from the Gibbs output Journal of the American Statistical Association 90 432 1995
11. S. Chib, and I. Jeliazkov Marginal likelihood from the Metropolis-Hastings output Journal of the American Statistical Association 96 453 2001 270 281
12. J. Eklund, and S. Karlsson Forecast combination and model averaging using predictive measures Econometric Reviews 26 2-4 2007 329 363
13. S. Frühwirth-Schnatter Markov chain Monte Carlo estimation of classical and dynamic switching and mixture models Journal of the American Statistical Association 96 453 2001 194 209
14. S. Frühwirth-Schnatter Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques Econometrics Journal 7 1 2004 143 167
15. S. Frühwirth-Schnatter, and H. Wagner Marginal likelihoods for non-Gaussian models using auxiliary mixture sampling Computational Statistics & Data Analysis 52 2008 4608 4624
16. A.E. Gelfand, and D.K. Dey Bayesian model choice: asymptotics and exact calculations Journal of the Royal Statistical Society. Series B (Methodological) 56 3 1994 501 514
17. A. Gelman, and X.L. Meng Simulating normalizing constants: from importance sampling to bridge sampling to path sampling Statistical Science 13 2 1998 163 185
18. S. Geman, and D. Geman Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images IEEE Transactions on Pattern Analysis and Machine Intelligence 6 1984 721 741
19. J. Geweke Bayesian inference in econometric models using Monte Carlo integration Econometrica 1989 1317 1339
20. J. Geweke Using simulation methods for Bayesian econometric models: inference, development, and communication Econometric Reviews 18 1 1999 1 73
21. C.J. Geyer Practical Markov chain Monte Carlo Statistical Science 1992 473 483
22. J.M. Hammersley, and D.C. Handscomb Monte Carlo Methods 1964 Methuen London
23. C. Han, and B.P. Carlin Markov chain Monte Carlo methods for computing Bayes factors Journal of the American Statistical Association 96 455 2001 1122 1132
24. W.K. Hastings Monte Carlo sampling methods using Markov chains and their applications Biometrika 57 1 1970 97 109
25. L.F. Hoogerheide, J.F. Kaashoek, and H.K. Van Dijk On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: an application of flexible sampling methods using neural networks Journal of Econometrics 139 1 2007 154 180
26. J.P. Hop, and H.K. Van Dijk SISAM and MIXIN: two algorithms for the computation of posterior moments and densities using Monte Carlo integration Computational Economics 5 3 1992 183 220
27. R.E. Kass, and A.E. Raftery Bayes factors Journal of the American Statistical Association 90 430 1995 773 795
28. T. Kloek, and H.K. Van Dijk Bayesian estimates of equation system parameters: an application of integration by Monte Carlo Econometrica 46 1 1978 1 19
29. Marske, D.; 1967. Biomedical oxygen demand data interpretation using sums of squares surface. Unpublished Master's Thesis. University of Wisconsin.
30. X.L. Meng, and S. Schilling Warp bridge sampling Journal of Computational & Graphical Statistics 11 3 2002 552 586
31. X.L. Meng, and W.H. Wong Simulating ratios of normalizing constants via a simple identity: a theoretical exploration Statistica Sinica 6 1996 831 860
32. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller Equation of state calculations by fast computing machines The Journal of Chemical Physics 21 6 1953 1087 1092
33. T. Miazhynskaia, and G. Dorffner A comparison of Bayesian model selection based on MCMC with an application to GARCH-type models Statistical Papers 47 4 2006 525 549
34. A. Mira, and G. Nicholls Bridge estimation of the probability density at a point Statistica Sinica 14 2 2004 603 612
35. W.K. Newey, and K.D. West A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix Econometrica 55 3 1987 703 708
36. M.A. Newton, and A.E. Raftery Approximate Bayesian inference with the weighted likelihood bootstrap Journal of the Royal Statistical Society. Series B (Methodological) 1994 3 48
37. C. Ritter, and M.A. Tanner Facilitating the Gibbs sampler: the Gibbs stopper and the Griddy-Gibbs sampler Journal of the American Statistical Association 87 419 1992 861 868
38. R Development Core Team (2008). R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL: http://www.R-project.org.
39. H.K. Van Dijk Some remarks on the simulation revolution in Bayesian econometric inference Econometric Reviews 18 1 1999 105 112
40. H.K. Van Dijk, and T. Kloek Further experience in Bayesian analysis using Monte Carlo integration Journal of Econometrics 14 3 1980 307 328
41. A.J. Zeevi, and R. Meir Density estimation through convex combinations of densities: approximation and estimation bounds Neural Networks 10 1 1997 99 109