Journal of Advanced Statistics

Download PDF (660.8 KB) PP. 109 - 116 Pub. Date: September 1, 2017

DOI: 10.22606/jas.2017.23001

• Arpita Chatterjee^*
  Department of Mathematical Sciences Georgia Southern University, Statesboro, GA, USA

Parametric models have been the dominant paradigm for Bayesian inferential works. This is mainly due to its simplicity and straightforward computations. However, given recent computational advances, Semiparametric Bayesian models have become increasingly popular to fit models under flexible distributional assumption. Dirichlet process mixture models form a particular class of Bayesian semiparametric models by assuming a random mixing distribution, taken to be a realization from a Dirichlet process. In this research, we show that even though hierarchical DP models provide flexibility in model fit, they may not perform uniformly better in other aspects as compared to the parametric models. If the DP model gives a better fit, then it should be used regardless of any effect it might have on the power. However, if it results in a reduction in power, then that is just the price of doing a good statistical analysis.

Semiparametric Bayesian, Dirichlet Process, Meta Analysis, Binary Data.

[1] Blackwell, D., and MacQueen, J. B. (1973). Ferguson distribution Via Pólya urn scheme. The Annals of Statistics, 1, 363–365.

[2] Burr, D., and Doss, H. (2005). A Bayesian semiparametric model for random-effects meta-analysis. Journal of the American Statistical Association, 100, 242–251.

[3] Escobar, M. D. (1994). Estimating normal means with a Dirichlet process prior. Journal of the American Statistical Association, 89, 268–277.

[4] Escobar, M. D., and West, M. (1995). Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association, 90, 577–588.

[5] Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. The Annals of Statistics, 1, 209–230.

[6] Ghosh, P., Nathoo, F., G¨onen, M., and Tiwari, R.C. ( 2011). Assessing noninferiority in a three-arm trial using the Bayesian approach. Statistics in Medicine 30, 1795–1808.

[7] Hardy, G. H., Littlewood J. E., and Pólya G. Inequalities. Cambridge Mathematical Library.

[8] Ishwaran, H., and Zarepour, M. (2002). Dirichlet prior sieves in finite normal mixtures. Statistica Sinica, 12, 941–963.

[9] Kaizar, E. E., Greenhouse, J. B., Seltman, H., and Kelleher, K. (2006). Do antidepressants cause suicidality in children? A Bayesian meta-analysis. Clinical Trials, 3, 73–98.

[10] Linero, A., and Daniels, M. J. (2015) A flexible Bayesian approach to monotone missing data in Longitudinal studies with nonignorable missingness With Application to an acute schizophrenia clinical trial. Journal of the American Statistical Association, 110.

[11] Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statistica Sinica, 4, 639–650.

[12] Sethuraman, J., and Tiwari, R. C. (1982). Convergence of Dirichlet measures and the interpretation of their parameter. Statistical Decision Theory and Related Topics III, eds. S. Gupta and J. O. Berger, New York: Springer-Verlag, pp. 305–315.

[13] Zhao, L., Shi, J., Shearon, T.H., and Li, Y. (2016). A Dirichlet process mixture model for survival outcome data: assessing nationwide kidney transplant centers. Statistics in Medicine, 34, 1404–1416.