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Comparing distributions using dependent normalized random measure mixtures

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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 (No.24).

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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...

Abstract

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

Official Date:

December 2010

Dates:

Date	Event
December 2010	Published

Volume:

Vol.2010

Number:

No.24

Number of Pages:

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Not Peer Reviewed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.