Corrigendum to “Using MCMC chain outputs to efficiently estimate Bayes factors” (J. Math. Psychol. (2011) 55 (367–378) (S0022249611000666)(10.1016/j.jmp.2011.06.004));Using MCMC chain outputs to efficiently estimate Bayes factors

Journal of Mathematical Psychology

Volumn 55, Issue 5, 2011, Pages 368-378

  Morey, Richard D ^a   Rouder, Jeffrey N ^b   Pratte, Michael S ^b   Speckman, Paul L ^b  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

^b UNIVERSITY OF MISSOURI   (United States)

Author keywords

ANOVA; Bayes factors; Bayesian inference; Bayesian statistics; Encompassing priors; Markov chain Monte Carlo

Indexed keywords

EID: 80053177568     PISSN: 00222496     EISSN: 10960880     Source Type: Journal    
DOI: 10.1016/j.jmp.2017.03.001     Document Type: Erratum

References (38)

1. Berger J.O., Sellke T. Testing a point null hypothesis: the irreconcilability of p values and evidence. Journal of the American Statistical Association 1987, 82(397):112-122. URL: http://www.jstor.org/stable/2289131.
2. Bernardo J.M., Smith A.F.M. Bayesian theory 2000, John Wiley & Sons, Chichester, England.
3. Blackwell D. Conditional expectation and unbiased sequential estimation. The Annals of Mathematical Statistics 1947, 18:105-110. 10.1214/aoms/1177730497.
4. Chen M.-H. Importance-weighted marginal Bayesian posterior density estimation. Journal of the American Statistical Association 1994, 89(427):818-824. URL: http://www.jstor.org/stable/2290907.
5. Chen, M.-H., & Shao, Q.-M. (1997). Performance study of marginal posterior density estimation via Kullback-Leibler divergence. Test 6, 321-350.
6. Chib S. Marginal likelihood from the Gibbs output. Journal of the American Statistical Association 1995, 90:1313-1321. URL: http://www.jstor.org/stable/2291521.
7. Dickey J.M. The weighted likelihood ratio, linear hypotheses on normal location parameters. The Annals of Mathematical Statistics 1971, 42(1):204-223. URL: http://www.jstor.org/stable/2958475.
8. Dickey J.M., Lientz B.P. The weighted likelihood ratio, sharp hypotheses about chances, the order of a Markov chain. The Annals of Mathematical Statistics 1970, 41(1):214-226. URL: http://www.jstor.org/stable/2239734.
9. Edwards W., Lindman H., Savage L.J. Bayesian statistical inference for psychological research. Psychological Review 1963, 70:193-242.
10. Gelfand A., Smith A.F.M. Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association 1990, 85:398-409.
11. Gelman A., Carlin J.B., Stern H.S., Rubin D.B. Bayesian data analysis 2004, Chapman and Hall, London. 2nd ed.
12. Geman S., Geman D. Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 1984, 6:721-741.
13. Heidelberger P., Welch P. Simulation run length control in the presence of an initial transient. Operations Research 1983, 31:1109-1144. URL: http://www.jstor.org/stable/170841.
14. Jeffreys H. Theory of probability 1961, Oxford University Press, New York. 3rd ed.
15. Kass R., Raftery A. Bayes factors. Journal of the American Statistical Association 1995, 90:773-795. URL: http://www.jstor.org/stable/2291091.
16. Klugkist I., Kato B., Hoijtink H. Bayesian model selection using encompassing priors. Statistica Neerlandica 2005, 59:57-69.
17. Kotz S., Nadarajah S. Multivariate t distributions and their applications 2004, Cambridge University Press, Cambridge.
18. Lee M.D. How cognitive modeling can benefit from hierarchical Bayesian models. Journal of Mathematical Psychology 2011, 55:1-7.
19. Liang F., Paulo R., Molina G., Clyde M.A., Berger J.O. Mixtures of g-priors for Bayesian variable selection. Journal of the American Statistical Association 2008, 103:410-423. URL: http://pubs.amstat.org/doi/pdf/10.1198/016214507000001337.
20. Lindley D.V. A statistical paradox. Biometrika 1957, 44:187-192.
21. Lunn D., Thomas A., Best N., Spiegelhalter D. WinBUGS-a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing 2000, 10:325-337.
22. Meng X., Wong W. Simulating ratios of normalizing constants via a simple identity: a theoretical exploration. Statistica Sinica 1996, 6:831-860.
23. Morey, R.D., & Rouder, J.N. (in press). Bayes factor approaches for testing interval null hypotheses. Psychological Methods.
24. Plummer, M. (2003). JAGS: a program for analysis of Bayesian graphical models using Gibbs sampling. In: Proceedings of the 3rd international workshop on distributed statistical computing.
25. R Development Core Team, (2009). R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0. URL: http://www.R-project.org.
26. Raftery A.E., Satagopan J.M., Newton M.A., Krivitsky P.N. Estimating the integrated likelihood via posterior simulation using the harmonic mean identity. Bayesian statistics 8 2007, 1-45. Oxford University Press, Alicante, Spain.
27. Roberts G. Markov chain concepts related to sampling algorithms. Markov chain Monte Carlo in practice 1996, Chapman and Hall, London. W. Gilks, S. Richardson, D. Spiegelhalter (Eds.).
28. Rouder J.N., Lu J. An introduction to Bayesian hierarchical models with an application in the theory of signal detection. Psychonomic Bulletin and Review 2005, 12:573-604.
29. Rouder J.N., Speckman P.L., Sun D., Morey R.D., Iverson G. Bayesian t-tests for accepting and rejecting the null hypothesis. Psychonomic Bulletin and Review 2009, 16:225-237.
30. Scott D.W. Multivariate density estimation 1992, John Wiley & Sons, New York.
31. Sellke T., Bayarri M.J., Berger J.O. Calibration of p values for testing precise null hypotheses. American Statistician 2001, 55:62-71. URL: http://www.jstor.org/stable/2685531.
32. Stone C.J., Hansen M.H., Kooperberg C., Truong Y.K. Polynomial splines and their tensor products in extended linear modeling. The Annals of Statistics 1997, 25(4):1371-1425. URL: http://www.jstor.org/stable/2959054.
33. Tanner M.A. Tools for statistical inference: methods for the exploration of posterior distributions and likelihood functions 1998, Springer, New York.
34. Verdinelli I., Wasserman L. Computing Bayes factors using a generalization of the Savage-Dickey density ratio. Journal of the American Statistical Association 1995, 90(430):614-618. URL: http://www.jstor.org/stable/2291073.
35. Wagenmakers E.-J., Lodewyckx T., Kuriyal H., Grasman R. Bayesian hypothesis testing for psychologists: a tutorial on the SavageDickey method. Cognitive Psychology 2010, 60:158-189.
36. Wetzels R., Raaijmakers J.G.W., Jakab E., Wagenmakers E.-J. How to quantify support for and against the null hypothesis: a flexible WinBUGS implementation of a default Bayesian ttest. Psychonomic Bulletin & Review 2009, 16:752-760.
37. Wetzels Ruud, Grasman Raoul P.P.P., Wagenmakers Eric-Jan An encompassing prior generalization of the Savage-Dickey density ratio. Computational Statistics and Data Analysis 2010, 54:2094-2102.
38. Zellner A., Siow A. Posterior odds ratios for selected regression hypotheses. Bayesian statistics: proceedings of the first international meeting held in Valencia (Spain) 1980, 585-603. University of Valencia. J.M. Bernardo, M.H. DeGroot, D.V. Lindley, A.F.M. Smith (Eds.).