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2015 | OriginalPaper | Buchkapitel

3. Density Estimation: Models Beyond the DP

verfasst von : Peter Müller, Fernando Andrés Quintana, Alejandro Jara, Tim Hanson

Erschienen in: Bayesian Nonparametric Data Analysis

Verlag: Springer International Publishing

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Abstract

The ubiquitous use of Dirichlet process models should not discourage researchers from considering interesting features of alternative models. In particular, the Polya tree model turns out to be an attractive choice for some applications. In this chapter we discuss the use of the Polya tree prior and its variations for density estimation. We define the model, introduce computation efficient methods for posterior inference and identify relative advantages and limitations compared with Dirichlet process models.

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Literatur
Zurück zum Zitat Argiento R, Guglielmi A, Pievatolo A (2010) Bayesian density estimation and model selection using nonparametric hierarchical mixtures. Comput Stat Data Anal 54(4):816–832MATHMathSciNetCrossRef Argiento R, Guglielmi A, Pievatolo A (2010) Bayesian density estimation and model selection using nonparametric hierarchical mixtures. Comput Stat Data Anal 54(4):816–832MATHMathSciNetCrossRef
Zurück zum Zitat Barrios E, Lijoi A, Nieto-Barajas LE, Prünster, I (2013) Modeling with normalized random measure mixture models. Stat Sci 28:313–334CrossRef Barrios E, Lijoi A, Nieto-Barajas LE, Prünster, I (2013) Modeling with normalized random measure mixture models. Stat Sci 28:313–334CrossRef
Zurück zum Zitat Berger J, Guglielmi A (2001) Bayesian testing of a parametric model versus nonparametric alternatives. J Am Stat Assoc 96:174–184MATHMathSciNetCrossRef Berger J, Guglielmi A (2001) Bayesian testing of a parametric model versus nonparametric alternatives. J Am Stat Assoc 96:174–184MATHMathSciNetCrossRef
Zurück zum Zitat Dubins LE, Freedman DA (1967) Random distribution functions. In: Proceedings of the fifth Berkeley symposium on mathematics, statistics and probability, vol 2, pp 183–214 Dubins LE, Freedman DA (1967) Random distribution functions. In: Proceedings of the fifth Berkeley symposium on mathematics, statistics and probability, vol 2, pp 183–214
Zurück zum Zitat Efromovich S (1999) Nonparametric curve estimation: methods, theory and applications. Springer, New YorkMATH Efromovich S (1999) Nonparametric curve estimation: methods, theory and applications. Springer, New YorkMATH
Zurück zum Zitat Hanson T, Kottas A, Branscum A (2008) Modelling stochastic order in the analysis of receiver operating characteristic data: Bayesian nonparametric approaches. J R Stat Soc Ser C 57:207–225MATHMathSciNetCrossRef Hanson T, Kottas A, Branscum A (2008) Modelling stochastic order in the analysis of receiver operating characteristic data: Bayesian nonparametric approaches. J R Stat Soc Ser C 57:207–225MATHMathSciNetCrossRef
Zurück zum Zitat James LF, Lijoi A, Prünster I (2009) Posterior analysis for normalized random measures with independent increments. Scand J Stat 36(1):76–97MATHMathSciNetCrossRef James LF, Lijoi A, Prünster I (2009) Posterior analysis for normalized random measures with independent increments. Scand J Stat 36(1):76–97MATHMathSciNetCrossRef
Zurück zum Zitat Jara A, Hanson T, Lesaffre E (2009) Robustifying generalized linear mixed models using a new class of mixture of multivariate Polya trees. J Comput Graph Stat 18:838–860MathSciNetCrossRef Jara A, Hanson T, Lesaffre E (2009) Robustifying generalized linear mixed models using a new class of mixture of multivariate Polya trees. J Comput Graph Stat 18:838–860MathSciNetCrossRef
Zurück zum Zitat Jara A, Hanson TE, Quintana FA, Müller P, Rosner GL (2011) DPpackage: Bayesian semi- and nonparametric modeling in R. J Stat Softw 40(5):1–30 Jara A, Hanson TE, Quintana FA, Müller P, Rosner GL (2011) DPpackage: Bayesian semi- and nonparametric modeling in R. J Stat Softw 40(5):1–30
Zurück zum Zitat Kingman JFC (1993) Poisson processes. Oxford University Press, New YorkMATH Kingman JFC (1993) Poisson processes. Oxford University Press, New YorkMATH
Zurück zum Zitat Lijoi A, Prünster I (2010) Models beyond the Dirichlet process. Cambridge University Press, Cambridge, pp 80–136 Lijoi A, Prünster I (2010) Models beyond the Dirichlet process. Cambridge University Press, Cambridge, pp 80–136
Zurück zum Zitat Lijoi A, Mena RH, Prünster I (2005) Hierarchical mixture modeling with normalized inverse-Gaussian priors. J Am Stat Assoc 100(472):1278–1291MATHCrossRef Lijoi A, Mena RH, Prünster I (2005) Hierarchical mixture modeling with normalized inverse-Gaussian priors. J Am Stat Assoc 100(472):1278–1291MATHCrossRef
Zurück zum Zitat Lijoi A, Mena RH, Prünster I (2007) Controlling the reinforcement in Bayesian non-parametric mixture models. J R Stat Soc Ser B (Stat Methodol) 69(4):715–740MathSciNetCrossRef Lijoi A, Mena RH, Prünster I (2007) Controlling the reinforcement in Bayesian non-parametric mixture models. J R Stat Soc Ser B (Stat Methodol) 69(4):715–740MathSciNetCrossRef
Zurück zum Zitat Metivier M (1971) Sur la construction de mesures aleatoires presque surement absolument continues par rapport a une mesure donnee. Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete 20:332–334MATHMathSciNetCrossRef Metivier M (1971) Sur la construction de mesures aleatoires presque surement absolument continues par rapport a une mesure donnee. Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete 20:332–334MATHMathSciNetCrossRef
Zurück zum Zitat Monticino M (2001) How to construct a random probability measure. Int Stat Rev 69:153–167MATHCrossRef Monticino M (2001) How to construct a random probability measure. Int Stat Rev 69:153–167MATHCrossRef
Zurück zum Zitat Paddock SM (1999) Randomized Polya trees: Bayesian nonparametrics for multivariate data analaysis. Unpublished doctoral thesis, Inistitute of Statistics and Decision Sciences, Duke University Paddock SM (1999) Randomized Polya trees: Bayesian nonparametrics for multivariate data analaysis. Unpublished doctoral thesis, Inistitute of Statistics and Decision Sciences, Duke University
Zurück zum Zitat Pitman J, Yor M (1997) The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann Probab 25:855–900MATHMathSciNetCrossRef Pitman J, Yor M (1997) The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann Probab 25:855–900MATHMathSciNetCrossRef
Zurück zum Zitat Regazzini E, Lijoi A, Prünster I (2003) Distributional results for means of normalized random measures with independent increments. Ann Stat 31(2):560–585MATHCrossRef Regazzini E, Lijoi A, Prünster I (2003) Distributional results for means of normalized random measures with independent increments. Ann Stat 31(2):560–585MATHCrossRef
Zurück zum Zitat Walker SG, Mallick BK (1997) Hierarchical generalized linear models and frailty models with Bayesian nonparametric mixing. J R Stat Soc Ser B 59:845–860MATHMathSciNetCrossRef Walker SG, Mallick BK (1997) Hierarchical generalized linear models and frailty models with Bayesian nonparametric mixing. J R Stat Soc Ser B 59:845–860MATHMathSciNetCrossRef
Metadaten
Titel
Density Estimation: Models Beyond the DP
verfasst von
Peter Müller
Fernando Andrés Quintana
Alejandro Jara
Tim Hanson
Copyright-Jahr
2015
DOI
https://doi.org/10.1007/978-3-319-18968-0_3