A default Bayesian hypothesis test for ANOVA designs

American Statistician

Volumn 66, Issue 2, 2012, Pages 104-111

  Wetzels, Ruud ^a   Grasman, Raoul P P P ^a   Wagenmakers, Eric Jan ^a  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

Bayes factor; Model selection; Teaching Bayesian statistics

Indexed keywords

EID: 84865148710     PISSN: 00031305     EISSN: None     Source Type: Journal    
DOI: 10.1080/00031305.2012.695956     Document Type: Article

References (57)

1. Abramowitz, M., and Stegun, I. (1972), Handbook of Mathematical Functions, New York: Dover. [107]
2. Ball, R. (2005), "Experimental Designs for Reliable Detection of Linkage Disequilibrium in Unstructured Random Population Association Studies, " Genetics, 170, 859-873. [104]
3. Bartlett, M. S. (1957), "A Comment on D. V. Lindley's Statistical Paradox, " Biometrika, 44, 533-534. [105]
4. Bayarri, M. J., and García-Donato, G. (2007), "Extending Conventional Priors forTestingGeneral Hypotheses inLinear Models, " Biometrika, 94, 135-152. [109]
5. Berger, J. (2006), "The Case for Objective Bayesian Analysis, " Bayesian Analysis, 1, 385-402. [105]
6. Berger, J. O., and Delampady, M. (1987), "Testing Precise Hypotheses, " Statistical Science, 2, 317-352. [105]
7. Berger, J. O., and Jefferys, W. H. (1992), "The Application of Robust Bayesian Analysis to Hypothesis Testing and Occam's Razor, " Statistical Methods and Applications, 1, 17-32. [110]
8. Berger, J. O., and Sellke, T. (1987), "Testing a Point Null Hypothesis: The Irreconcilability of p Values and Evidence, " Journal of the American Statistical Association, 82, 112-139. [105,108]
9. Bernardo, J. M., and Smith, A. F. M. (1994), Bayesian Theory, New York: Wiley. [104]
10. Box, G. E. P., and Tiao, G. C. (1973), Bayesian Inference in Statistical Analysis, Reading: Addison-Wesley. [107,108]
11. Casella, G., and Moreno, E. (2006), "Objective Bayesian Variable Selection, " Journal of the American Statistical Association, 101, 157-167. [109]
12. Chipman, H. (1996), "Bayesian Variable Selection with Related Predictors, " Canadian Journal of Statistics, 24, 17-36. [105]
13. Clyde, M. (1999), "Bayesian Model Averaging and Model Search Strategies" (with discussion), Bayesian Statistics, 6, 157-185. [109]
14. Cui, W., and George, E. (2008), "Empirical Bayes vs. Fully Bayes Variable Selection, " Journal of Statistical Planning and Inference, 138, 888-900. [107]
15. Dellaportas, P., Forster, J., and Ntzoufras, I. (in press), "Joint Specification of Model Space and Parameter Space Prior Distributions, " Statistical Science, in press. [107]
16. Dickey, J. M. (1971), "The Weighted Likelihood Ratio, Linear Hypotheses on Normal Location Parameters, " The Annals of Mathematical Statistics, 42, 204-223. [105]
17. Draper, N., and Smith, H. (1998), Applied Regression Analysis, New York: Wiley-Interscience. [104,105]
18. Edwards, W., Lindman, H., and Savage, L. J. (1963), "Bayesian Statistical Inference for Psychological Research, " Psychological Review, 70, 193-242. [108]
19. Faraway, J. (2002), "Practical Regression and ANOVA using R, " available at http://cran.r-project.org/doc/contrib/Faraway-PRA.pdf. [104,108,109]
20. Fernandez, C., Ley, E., and Steel, M. (2001), "Benchmark Priors for Bayesian Model Averaging, " Journal of Econometrics, 100, 381-427. [106]
21. Foster, D., and George, E. (1994), "The Risk Inflation Criterion for Multiple Regression, " The Annals of Statistics, 22, 1947-1975. [106]
22. Gelman, A. (2008), "Objections to Bayesian Statistics, " Bayesian Analysis, 3, 445-450. [105]
23. Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2004), Bayesian Data Analysis (2nd ed.), Boca Raton, FL: Chapman & Hall/CRC. [104]
24. George, E., and McCulloch, R. (1997), "Approaches for Bayesian Variable Selection, " Statistica Sinica, 7, 339-373. [105,109]
25. Gönen, M., Johnson, W. O., Lu, Y., and Westfall, P. H. (2005), "The Bayesian Two-Sample t test, " The American Statistician, 59, 252-257. [104,109]
26. Hoeting, J. A., Madigan, D., Raftery, A. E., and Volinsky, C. T. (1999), "Bayesian Model Averaging: A Tutorial, " Statistical Science, 14, 382-417. [109]
27. Ishwaran, H., and Rao, J. (2003), "Detecting Differentially Expressed Genes in Microarrays using Bayesian Model Selection, " Journal of the American Statistical Association, 98, 438-455. [104]
28. Jeffreys, H. (1961), Theory of Probability, Oxford, UK: Oxford University Press. [105,106]
29. Kass, R. E., and Raftery, A. E. (1995), "Bayes Factors, " Journal of the American Statistical Association, 90, 377-395. [105]
30. Kass, R. E., andWasserman, L. (1995), "A Reference Bayesian Test for Nested Hypotheses and Its Relationship to the Schwarz Criterion, " Journal of the American Statistical Association, 90, 928-934. [106]
31. Kaufman, C. G., and Sain, S. R. (2010), "Bayesian Functional ANOVA Modeling Using Gaussian Process Prior Distributions, " Bayesian Analysis, 5, 123-150. [104]
32. Kuo, L., and Mallick, B. (1998), "Variable Selection for Regression Models, " Sankhya: The Indian Journal of Statistics, Series B, 60, 65-81. [109]
33. Leamer, E. (1978), "Regression Selection Strategies and Revealed Priors, " Journal of the American Statistical Association, 73, 580-587. [105]
34. Liang, F., Paulo, R., Molina, G., Clyde, M., and Berger, J. (2008), "Mixtures of g Priors for Bayesian Variable Selection, " Journal of the American Statistical Association, 103, 410-423. [104,106,107]
35. Lindley, D. (1980), "L. J. Savage-HisWork in Probability and Statistics, " The Annals of Statistics, 8, 1-24. [105]
36. Lindley, D. V. (2000), "The Philosophy of Statistics, " The Statistician, 49, 293-337. [104]
37. Maruyama, Y. (2009), "A Bayes Factor with Reasonable Model Selection Consistency for ANOVA Model, " Arxiv preprint arXiv:0906.4329. [104]
38. Mitchell, T., and Beauchamp, J. (1988), "Bayesian Variable Selection in Linear Regression, " Journal of the American Statistical Association, 83, 1023-1032. [105,109]
39. Ntzoufras, I. (2009), BayesianModeling UsingWinBUGS, Hoboken, NJ:Wiley. [104]
40. O'Hagan, A., and Forster, J. (2004), Kendall's Advanced Theory of Statistics Vol. 2B: Bayesian Inference (2nd ed.), London: Arnold. [104]
41. O'Hara, R., and Sillanp̈äa, M. (2009), "AReviewof BayesianVariable Selection Methods: What, How and Which, " Bayesian Analysis, 4, 85-118. [109]
42. Poirier, D. J. (2006), "The Growth of Bayesian Methods in Statistics and Economics Since 1970, " Bayesian Analysis, 1, 969-980. [104]
43. Press, S., Chib, S., Clyde, M., Woodworth, G., and Zaslavsky, A. (2003), Subjective and Objective Bayesian Statistics: Principles, Models, and Applications, New York: Wiley-Interscience. [105]
44. Qian, S., and Shen, Z. (2007), "Ecological Applications of Multilevel Analysis of Variance, " Ecology, 88, 2489-2495. [104]
45. R Development Core Team. (2004), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing, ISBN 3-900051-00-3. [107]
46. Robert, C. (1993), "A Note on Jeffreys-Lindley Paradox, " Statistica Sinica, 3, 601-608. [105]
47. Scott, J., and Berger, J. (2010), "Bayes and Empirical-Bayes Multiplicity Adjustment in the Variable-Selection Problem, " The Annals of Statistics, 38, 2587-2619. [110]
48. Sellke, T., Bayarri, M. J., and Berger, J. O. (2001), "Calibration of p Values for Testing Precise Null Hypotheses, " The American Statistician, 55, 62-71. [108]
49. Sen, S., and Churchill, G. (2001), "A Statistical Framework for Quantitative Trait Mapping, " Genetics, 159, 371-287. [104]
50. Shafer, G. (1982), "Lindley's Paradox, " Journal of the American Statistical Association, 77, 325-351. [105]
51. Stephens, M., and Balding, D. J. (2009), "Bayesian Statistical Methods for Genetic Association Studies, " Nature Reviews Genetics, 10, 681-690. [110]
52. Strawderman, W. (1971), "Proper Bayes Minimax Estimators of the Multivariate Normal Mean, " The Annals of Mathematical Statistics, 42, 385-388. [107]
53. Westfall, P., and Gönen, M. (1996), "Asymptotic Properties of ANOVA Bayes Factors, " Communications in Statistics-Theory and Methods, 25, 3101-3123. [104]
54. Zellner, A. (1986), "On Assessing Prior Distributions and Bayesian Regression Analysis with g-Prior Distributions, " in Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, eds. P. K. Goel and A. Zellner, pp. 233-243. [105]
55. Zellner, A. (1987), An Introduction to Bayesian Inference in Econometrics, Malabar, FL: RE Krieger Pub. Co. [105]
56. Zellner, A., and Siow, A. (1980), "PosteriorOdds Ratios for Selected Regression Hypotheses, " in Bayesian Statistics, eds. J. M. Bernardo, M. H. DeGroot, D. V. Lindley, and A. F. M. Smith, Valencia: University Press, pp. 585-603. [106]
57. Zeugner, S., and Feldkircher, M. (2009), "Benchmark Priors Revisited: On Adaptive Shrinkage and the Supermodel Effect in Bayesian Model Averaging, " IMF Working Papers, 9, 202. [107]