Browse > Article

Default Bayesian testing for the bivariate normal correlation coefficient  

Kang, Sang-Gil (Department of Computer and Data Information, Sangji University)
Kim, Dal-Ho (Department of Statistics, Kyungpook National University)
Lee, Woo-Dong (Department of Asset Management, Daegu Haany University)
Publication Information
Journal of the Korean Data and Information Science Society / v.22, no.5, 2011 , pp. 1007-1016 More about this Journal
Abstract
This article deals with the problem of testing for the correlation coefficient in the bivariate normal distribution. We propose Bayesian hypothesis testing procedures for the bivariate normal correlation coefficient under the noninformative prior. The noninformative priors are usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. A simulation study and an example are provided.
Keywords
Bivariate normal distribution; correlation coefficient; fractional Bayes factor; intrinsic Bayes factor; reference prior;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 O'Hagan, A. (1995). Fractional Bayes factors for model comparison (with discussion). Journal of Royal Statistical Society B, 57, 99-118.
2 O'Hagan, A. (1997). Properties of intrinsic and fractional Bayes factors. Test, 6, 101-118.   DOI   ScienceOn
3 Ruben, H. (1966). Some new results on the distribution of the sample correlation coefficient. Journal of Royal Statistical Society B, 28, 513-525.
4 Berger, J. O. and Pericchi, L. R. (2001). Objective Bayesian methods for model selection: Introduction and comparison (with discussion). In Model Selection, Institute of Mathematical Statistics Lecture Notes-Monograph Series, 38, edited by P. Lahiri, 135-207, Beachwood, Ohio.
5 Berger, J. O. and Sun, D. (2008). Objective priors for a bivariate normal model. The Annals of Statistics, 36, 963-982.   DOI   ScienceOn
6 Fisher, R. A. (1915). Frequency distribution of the values of the correlation coecient in samples from an indefinitely large population. Biometrika, 10, 507-521.
7 Ghosh, M., Mukherjee, B., Santra, U. and Kim, D. (2010). Bayesian and likekihood-based inference for the bivariate normal correlation coefficient. Journal of Statistical Planning and Inference, 140, 1410-1416.   DOI   ScienceOn
8 Hotelling, H. (1953). New light on the correlation coefficient and its transform. Journal of Royal Statistical Society B, 15, 193-232.
9 Berger, J. O. and Bernardo, J. M. (1989). Estimating a product of means : Bayesian analysis with reference priors. Journal of the American Statistical Association, 84, 200-207.   DOI   ScienceOn
10 Berger, J. O. and Bernardo, J. M. (1992). On the development of reference priors (with discussion). In Bayesian Statistics IV, edited by J. M. Bernardo et al., Oxford University Press, Oxford, 35-60.
11 Berger, J. O. and Pericchi, L. R. (1996). The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association, 91, 109-122.   DOI   ScienceOn
12 Levine, J. A., Eberhardt, N. L. and Jensen, M. D. (1999). Role of nonexercise activity thermogenesis in resistance to fat gain in human. Science, 283, 212-214.   DOI
13 Berger, J. O. and Pericchi, L. R. (1998). Accurate and stable Bayesian model selection: The median intrinsic Bayes factor. Sankya B, 60, 1-18.
14 Spiegelhalter, D. J. and Smith, A. F. M. (1982). Bayes factors for linear and log-linear models with vague prior information. Journal of Royal Statistical Society B, 44, 377-387.
15 Sun, Y. and Wong, A. C. M. (2007). Interval estimation for the normal correlation coefficient. Statistics & Probability Letters, 77, 1652-1661.   DOI   ScienceOn
16 Kang, S. G., Kim, D. H. and Lee, W. D. (2006). Bayesian one-sided testing for the ratio of Poisson means. Journal of the Korean Data & Information Science Society, 17, 619-631.
17 Kang, S. G., Kim, D. H. and Lee, W. D. (2008). Bayesian model selection for inverse Gaussian populations with heterogeneity. Journal of the Korean Data & Information Science Society, 19, 621-634.
18 Kang, S. G., Kim, D. H. and Lee, W. D. (2010). Default Bayesian testing for normal mean with known coefficient of variation. Journal of the Korean Data & Information Science Society, 21, 297-308.