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H. Ishwaran, Lancelot James (2001)
Gibbs Sampling Methods for Stick-Breaking PriorsJournal of the American Statistical Association, 96
D. Berry, R. Christensen (1979)
Empirical Bayes Estimation of a Binomial Parameter Via Mixtures of Dirichlet ProcessesAnnals of Statistics, 7
Jun Liu (1996)
Nonparametric hierarchical Bayes via sequential imputationsAnnals of Statistics, 24
Lancelot James (2006)
Spatial Neutral to the Right Species Sampling Mixture Models. Appears as an invited contribution
Hartigan Hartigan (1990)
Partition modelsCommuns Statist. Theory Meth., 19
C. Charalambides (2005)
Combinatorial Methods in Discrete Distributions: Charalambides/Combinatorial
J. Doornik (1996)
Object-orientd matrix programming using OX
H. Ishwaran, Lancelot James (2003)
Generalized weighted Chinese restaurant processes for species sampling mixture modelsStatistica Sinica, 13
J. Kingman (1975)
Random Discrete DistributionsJournal of the royal statistical society series b-methodological, 37
E. Regazzini, A. Lijoi, Igor Prünster (2003)
Distributional results for means of normalized random measures with independent incrementsAnnals of Statistics, 31
F. Quintana, P. Iglesias (2003)
Bayesian clustering and product partition modelsJournal of the Royal Statistical Society: Series B (Statistical Methodology), 65
S. MacEachern (1994)
Estimating normal means with a conjugate style dirichlet process priorCommunications in Statistics - Simulation and Computation, 23
Christopher Bush, S. MacEachern (1996)
A semiparametric Bayesian model for randomised block designsBiometrika, 83
S. MacEachern, P. Müller (1998)
Estimating mixture of dirichlet process modelsJournal of Computational and Graphical Statistics, 7
J. Pitman (2006)
Combinatorial Stochastic Processes, 1875
I. Pruenster (2003)
Random probability measures derived from increasing additive processes and their application to Bayesian statistics.
C. Charalambides, Jagbir Singh (1988)
Review of the stirling numbers, their generalizations and Statistical ApplicationsCommunications in Statistics-theory and Methods, 17
J. Pitman (2002)
Poisson-Kingman partitionsarXiv: Probability
Epifani Epifani, Lijoi Lijoi, Prünster Prünster (2003)
Exponential functionals and means of neutral‐to‐the‐right priorsBiometrika, 90
J. Pitman (1995)
Exchangeable and partially exchangeable random partitionsProbability Theory and Related Fields, 102
S. MacEachern (1998)
Computational Methods for Mixture of Dirichlet Process Models
J. Marin, K. Mengersen, C. Robert (2005)
Bayesian Modelling and Inference on Mixtures of DistributionsHandbook of Statistics, 25
Regazzini Regazzini, Lijoi Lijoi, Prünster Prünster (2003)
Distributional results for means of random measures with independent incrementsAnn. Statist., 31
P. Green, S. Richardson (2001)
Modelling Heterogeneity With and Without the Dirichlet ProcessScandinavian Journal of Statistics, 28
Michael Newton, Michael New~on (2008)
On a Class of Bayesian Nonparametric Estimates : I . Density Estimates
N. Hjort (2000)
Bayesian analysis for a generalised Dirichlet process prior
C. Charalambides (2005)
Combinatorial Methods in Discrete Distributions
Lancelot James (2007)
NEUTRAL-TO-THE-RIGHT SPECIES SAMPLING MIXTURE MODELS
R. Keener (2009)
Probability and Measure
Lancelot James (2002)
Poisson Process Partition Calculus with applications to Exchangeable models and Bayesian NonparametricsarXiv: Probability
D. Barry, J. Hartigan (1993)
A Bayesian Analysis for Change Point ProblemsJournal of the American Statistical Association, 88
C. Antoniak (1974)
Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric ProblemsAnnals of Statistics, 2
Sonia Petrone, A. Raftery (1997)
A note on the Dirichlet process prior in Bayesian nonparametric inference with partial exchangeabilityStatistics & Probability Letters, 36
W. Ewens (1972)
The sampling theory of selectively neutral alleles.Theoretical population biology, 3 1
F. Quintana (1998)
Nonparametric Bayesian Analysis for Assessing Homogeneity in k × l Contingency Tables with Fixed Right Margin TotalsJournal of the American Statistical Association, 93
R. Korwar, M. Hollander (1973)
Contributions to the Theory of Dirichlet ProcessesAnnals of Probability, 1
A. Gnedin, J. Pitman (2004)
Exchangeable Gibbs partitions and Stirling trianglesJournal of Mathematical Sciences, 138
J. Pitman (1996)
Some developments of the Blackwell-MacQueen urn scheme
Kingman Kingman (1975)
Random discrete distributions (with discussion)J. R. Statist. Soc. B, 37
(1999)
Dependent nonparametric processes
M. Iorio, P. Müller, G. Rosner, S. MacEachern (2004)
An ANOVA Model for Dependent Random MeasuresJournal of the American Statistical Association, 99
R. Arratia, A. Barbour, S. Tavaré (2003)
Logarithmic Combinatorial Structures: A Probabilistic Approach
A. Lijoi, R. Mena, Igor Prünster (2005)
Hierarchical Mixture Modeling With Normalized Inverse-Gaussian PriorsJournal of the American Statistical Association, 100
Lancelot James, A. Lijoi, I. Pruenster (2005)
Bayesian Inference Via Classes of Normalized Random MeasuresEconometrics eJournal
Lancelot James (2003)
Poisson Calculus for Spatial Neutral to the Right Processes
A. Brix (1999)
Generalized Gamma measures and shot-noise Cox processesAdvances in Applied Probability, 31
M. Escobar, M. West (1995)
Bayesian Density Estimation and Inference Using MixturesJournal of the American Statistical Association, 90
Gnedin Gnedin, Pitman Pitman (2005)
Exchangeable Gibbs partitions and Stirling trianglesZap. Nauchn. Sem. St Peterburg. Otdel. Mat. Inst. Steklov., 325
I. Epifani, A. Lijoi, I. Prnster (2003)
Exponential functionals and means of neutral-to-the-right priors Biometrika 90
SummaryThe paper deals with the problem of determining the number of components in a mixture model. We take a Bayesian non-parametric approach and adopt a hierarchical model with a suitable non-parametric prior for the latent structure. A commonly used model for such a problem is the mixture of Dirichlet process model. Here, we replace the Dirichlet process with a more general non-parametric prior obtained from a generalized gamma process. The basic feature of this model is that it yields a partition structure for the latent variables which is of Gibbs type. This relates to the well-known (exchangeable) product partition models. If compared with the usual mixture of Dirichlet process model the advantage of the generalization that we are examining relies on the availability of an additional parameter σ belonging to the interval (0,1): it is shown that such a parameter greatly influences the clustering behaviour of the model. A value of σ that is close to 1 generates a large number of clusters, most of which are of small size. Then, a reinforcement mechanism which is driven by σ acts on the mass allocation by penalizing clusters of small size and favouring those few groups containing a large number of elements. These features turn out to be very useful in the context of mixture modelling. Since it is difficult to specify a priori the reinforcement rate, it is reasonable to specify a prior for σ. Hence, the strength of the reinforcement mechanism is controlled by the data.
Journal of the Royal Statistical Society Series B (Statistical Methodology) – Oxford University Press
Published: Aug 7, 2007
Keywords: Bayesian clustering; Bayesian non-parametric inference; Dirichlet process; Mixture model; Predictive distribution; Product partition model
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