On Bayesian nonparametric modelling of two correlated distributions
Kolossiatis, Michalis, Griffin, Jim E. and Steel, Mark F. J. (2010) On Bayesian nonparametric modelling of two correlated distributions. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers).
WRAP_Kolossiatis_10-22w.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
In this paper, we consider the problem of modelling a pair of related distributions using Bayesian nonparametric methods. A representation of the distributions as weighted sums of distributions is derived through normalisation. This allows us to define several classes of nonparametric priors. The properties of these distributions are explored and efficient Markov chain Monte Carlo methods are developed. The methodology is illustrated on simulated data and an example concerning hospital efficiency measurement.
|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), Bayesian statistical decision theory, Hospitals -- Mathematical models, Nonparametric statistics|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Number of Pages:||27|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|References:||D. Aigner, C. A. K. Lovell, and P. Schmidt. Formulation and estimation of stochastic frontier production function models. J. Econometrics, 6:21–37, 1977. J.-M. Bernardo and A. F. M. Smith. Bayesian theory. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons Ltd., Chichester, 1994. T. S. Ferguson. A Bayesian analysis of some nonparametric problems. Ann. Statist., 1:209–230, 1973. C. Fern´andez, J. Osiewalski, and M. F. J. Steel. On the use of panel data in stochastic frontier models with improper priors. J. Econometrics, 79:169–193, 1997. J. E. Griffin and M. F. J. Steel. Semiparametric Bayesian inference for stochastic frontier models. J. Econometrics, 123:121–152, 2004. J. E. Griffin, M. Kolossiatis, and M. F. J. Steel. Comparing distributions with dependent normalized random measure mixtures, mimeo, 2010. H. Ishwaran and M. Zarepour. Series representations for multivariate generalized gamma processes via a scale invariance principle. Stat. Sinica, 19:1665–1682, 2009. L. F. James, A. Lijoi, and I. Pruenster. Bayesian inference via classes of normalized random measures, mimeo, 2005. G. Koop, J. Osiewalski, and M. F. J. Steel. Bayesian efficiency analysis through individual effects: Hospital cost frontiers. J. Econometrics, 76:77–105, 1997. F. Leisen and A. Lijoi. Vectors of two-parameter Poisson-Dirichlet processes, mimeo, 2010. W. Meeusen and J. van den Broeck. Efficiency estimation from Cobb-Douglas production functions with composed error. Int. Econ. Review, 18:435–44, 1977. P. M¨uller, F. Quintana, and G. Rosner. A method for combining inference across related nonparametric Bayesian models. J. R. Stat. Soc. Ser. B, 66:735–749, 2004. V. Rao and Y. W. Teh. Spatial normalized gamma processes. In Y. Bengio, D. Schuurmans, J. Lafferty, C. K. I. Williams, and A. Culotta, editors, Advances in Neural Information Processing Systems 22, pages 1554–1562. 2009. Y. W. Teh, M. I. Jordan, M. J. Beal, and D. M. Blei. Hierarchical Dirichlet processes. J. Amer. Statist. Assoc., 101(476):1566–1581, 2006. S. G. Walker and P. Muliere. A bivariate Dirichlet process. Stat. Probab. Letters, 64: 1–7, 2003.|
Actions (login required)