Comparing distributions using dependent normalized random measure mixtures
Griffin, Jim E., Kolossiatis, Michalis and Steel, Mark F. J. (2010) Comparing distributions using dependent normalized random measure mixtures. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers, Vol.2010).
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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
A methodology for the simultaneous Bayesian nonparametric modelling of several distributions is developed. Our approach uses normalized random measures with independent increments and builds dependence through the superposition of shared processes. The properties of the prior are described and the modelling possibilities of this framework are explored in some detail. Efficient slice sampling methods are developed for inference. Various posterior summaries are introduced which allow better understanding of the differences between distributions. The methods are illustrated on simulated data and examples from survival analysis and stochastic frontier analysis.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Distribution (Probability theory), Random measures|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Number of Pages:||33|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|References:||Beadle, G., S. Come, C. Henderson, B. Silver, and S. Hellman (1984). The effect of adjuvant chemotherapy on the cosmetic results after primary radiation treatment for early stage breast cancer. Inter. J. Rad. Oncol., Biol. Phys. 10, 2131–2137. Brix, A. (1999). Generalized gamma measures and shot-noise Cox processes. Adv. in Appl. Probab. 31, 929–953. De Iorio, M., P. M¨uller, G. L. Rosner, and S. N. MacEachern (2004). An ANOVA Model for Dependent Random Measures. J. Amer. Statist. Assoc. 99, 205–215. Doss, H. and F.W. Huffer (2003). Monte Carlo methods for Bayesian analysis of survival data using mixtures of Dirichlet process prior. J. Comput. Graph. Statist. 12, 282–307. Dunson, D. B., Y. Xue, and L. Carin (2008). The matrix stick breaking process: Flexible Bayes meta analysis. J. Amer. Statist. Assoc. 103, 317–327. Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1, 209–230. Griffin, J. E. (2009). The Ornstein-Uhlenbeck Dirichlet Process and other time-varying nonparametric priors. Technical report, University of Warwick. Griffin, J. E. and P. J. Brown (2010). Inference with Normal-Gamma prior distributions in regression problems. Bayesian Analysis 5, 171–188. Griffin, J. E. and M. F. J. Steel (2004). Semiparametric Bayesian inference for stochastic frontier models. J. Econometrics 123, 121–152. Griffin, J. E. and S. G. Walker (2010). Posterior simulation of Normalised Random Measure mixtures. J. Comput. Graph. Statist., forthcoming. James, L. F., A. Lijoi, and I. Pr¨unster (2009). Posterior analysis for normalized random measures with independent increments. Scand. J. Statist. 36, 76–97. Kalli, M., J. E. Griffin, and S. G. Walker (2011). Slice sampling mixture models. Statistics and Computing 21, forthcoming. Kingman, J. (1975). Random discrete distributions. J. R. Stat. Soc. Ser. B 37, 1–22 (with discussion). Kolossiatis, M., J. E. Griffin, and M. F. J. Steel (2010). On Bayesian nonparametric modelling of two correlated distributions. Technical report, University of Warwick. Koop, G., J. Osiewalski, and M. F. J. Steel (1997). Bayesian efficiency analysis through individual effects: Hospital cost frontiers. J. Econometrics 76, 77–105. Lijoi, A., R. H. Mena, and I. Pr¨unster (2005). Hierarchical mixture modeling with normalized inverse-Gaussian priors. J. Amer. Statist. Assoc. 100, 1278–1291. Lijoi, A., R. H. Mena, and I. Pr¨unster (2007). Controlling the reinforcement in Bayesian non-parametric mixture models. J. R. Stat. Soc. Ser. B 69, 715–740. M¨uller, P., F. Quintana, and G. Rosner (2004). A method for combining inference across related nonparametric Bayesian models. J. R. Stat. Soc. Ser. B 66, 735–749. Rodriguez, A., D. Dunson, and J. Taylor (2009). Bayesian hierarchically weighted finite mixture models for samples of distributions. Biostatistics 10, 155–171. Scott, J. G. and N. G. Polson (2011). Shrink globally, act locally: Sparse Bayesian regularization and prediction. In Bayesian Statistics 9. Oxford University Press. Teh, Y. W., M. I. Jordan, M. J. Beal, and D. M. Blei (2006). Hierarchical Dirichlet processes. J. Amer. Statist. Assoc. 101, 1566–1581.|
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