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Theory and Methods

Hierarchical Normalized Completely Random Measures to Cluster Grouped Data

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Pages 318-333 | Received 21 May 2018, Accepted 07 Mar 2019, Published online: 17 May 2019

References

  • Argiento, R., Bianchini, I., and Guglielmi, A. (2016), “Posterior Sampling From ε-Approximation of Normalized Completely Random Measure Mixtures,” Electronic Journal of Statistics, 10, 3516–3547. DOI: 10.1214/16-EJS1168.
  • Argiento, R., Cremaschi, A., and Guglielmi, A. (2014), “A ‘Density-Based’ Algorithm for Cluster Analysis Using Species Sampling Gaussian Mixture Models,” Journal of Computational and Graphical Statistics, 23, 1126–1142. DOI: 10.1080/10618600.2013.856796.
  • Bassetti, F., Casarin, R., and Rossini, L. (2018), “Hierarchical Species Sampling Models,” arXiv no. 1803.05793.
  • Blei, D. M. (2012), “Probabilistic Topic Models,” Communications of the ACM, 55, 77–84. DOI: 10.1145/2133806.2133826.
  • Camerlenghi, F., Lijoi, A., Orbanz, P., and Prünster, I. (2019), “Distribution Theory for Hierarchical Processes,” The Annals of Statistics, 47, 67–92. DOI: 10.1214/17-AOS1678.
  • Camerlenghi, F., Lijoi, A., and Prünster, I. (2017), “Bayesian Prediction With Multiple-Samples Information,” Journal of Multivariate Analysis, 156, 18–28. DOI: 10.1016/j.jmva.2017.01.010.
  • Durrett, R. (1991), Probability: Theory and Examples, Pacific Grove, CA: Wadsworth & Brooks/Cole.
  • Favaro, S., and Teh, Y. (2013), “MCMC for Normalized Random Measure Mixture Models,” Statistical Science, 28, 335–359. DOI: 10.1214/13-STS422.
  • Ferguson, T. S. (1983), “Bayesian Density Estimation by Mixtures of Normal Distributions,” in Recent Advances in Statistics: Papers in Honor of Herman Chernoff on His Sixtieth Birthday, eds. M. Rizvi, J. Rustagi and D. Siegmund, 287–302. New York: Academic Press, Inc.
  • Hoff, P. D. (2009), A First Course in Bayesian Statistical Methods, New York: Springer Verlag.
  • Ishwaran, H., and James, L. F. (2001), “Gibbs Sampling Methods for Stick-Breaking Priors,” Journal of the American Statistical Association, 96, 161–173. DOI: 10.1198/016214501750332758.
  • Ishwaran, H., and James, L. F. (2003), “Generalized Weighted Chinese Restaurant Processes for Species Sampling Mixture Models,” Statistica Sinica, 13, 1211–1235.
  • James, L. F., Lijoi, A., and Prünster, I. (2009), “Posterior Analysis for Normalized Random Measures With Independent Increments,” Scandinavian Journal of Statistics, 36, 76–97. DOI: 10.1111/j.1467-9469.2008.00609.x.
  • Kallenberg, O. (2005), Probabilistic Symmetries and Invariance Principles, New York: Springer.
  • Kingman, J. F. C. (1993), Poisson Processes (Vol. 3), Oxford: Oxford University Press.
  • Lau, J. W., and Green, P. J. (2007), “Bayesian Model-Based Clustering Procedures,” Journal of Computational and Graphical Statistics, 16, 526–558. DOI: 10.1198/106186007X238855.
  • Lijoi, A., Mena, R. H., and Prünster, I. (2007), “Controlling the Reinforcement in Bayesian Non-parametric Mixture Models,” Journal of the Royal Statistical Society, Series B, 69, 715–740. DOI: 10.1111/j.1467-9868.2007.00609.x.
  • Lijoi, A., and Prünster, I. (2010), “Models Beyond the Dirichlet Process,” in Bayesian Nonparametrics, eds. N. Hjort, C. Holmes, P. Müller, and S. Walker, Cambridge: Cambridge University Press, pp. 80–136.
  • Lo, A. Y. (1984), “On a Class of Bayesian Nonparametric Estimates: I. Density Estimates,” The Annals of Statistics, 12, 351–357. DOI: 10.1214/aos/1176346412.
  • MacEachern, S. N. (1999), “Dependent Nonparametric Processes,” in ASA Proceedings of the Section on Bayesian Statistical Science, pp. 50– 55.
  • Malsiner-Walli, G., Frühwirth-Schnatter, S., and Grün, B. (2017), “Identifying Mixtures of Mixtures Using Bayesian Estimation,” Journal of Computational and Graphical Statistics, 26, 285–295. DOI: 10.1080/10618600.2016.1200472.
  • Müller, P., and Quintana, F. (2010), “Random Partition Models With Regression on Covariates,” Journal of Statistical Planning and Inference, 140, 2801–2808. DOI: 10.1016/j.jspi.2010.03.002.
  • Neal, R. M. (2000), “Markov Chain Sampling Methods for Dirichlet Process Mixture Models,” Journal of Computational and Graphical Statistics, 9, 249–265. DOI: 10.2307/1390653.
  • Pinheiro, J., and Bates, D. (2000), Mixed-Effects Models in S and S-PLUS, New York: Springer.
  • Pitman, J. (1996), “Some Developments of the Blackwell-MacQueen Urn Scheme,” in Statistics, Probability and Game Theory: Papers in Honor of David Blackwell, eds. T. S. Ferguson, L. S. Shapley and J. B. MacQueen, vol. 30, 245–267. Hayward: Institute of Mathematical Statistics.
  • Pitman, J. (2003), “Poisson-Kingman Partitions,” in Science and Statistics: A Festschrift for Terry Speed, IMS Lecture Notes-Monograph Series (Vol. 40), Hayward, CA: Institute of Mathematical Statistics, pp 1–34.
  • Pitman, J. (2006), Combinatorial Stochastic Processes, Lecture Notes-Monograph Series (Vol. 1875), New York: Springer.
  • Regazzini, E., Lijoi, A., and Prünster, I. (2003), “Distributional Results for Means of Normalized Random Measures With Independent Increments,” The Annals of Statistics, 31, 560–585. DOI: 10.1214/aos/1051027881.
  • Teh, Y. W. and Jordan, M. I. (2010), “Hierarchical Bayesian Nonparametric Models with Applications,” in Bayesian Nonparametrics, eds. N. Hjort, C. Holmes, P. Müller and Walker, 158–207. Cambridge: Cambridge University Press.
  • Teh, Y. W., Jordan, M. I., Beal, M. J., and Blei, D. M. (2005), “Sharing Clusters Among Related Groups: Hierarchical Dirichlet Processes,” in Advances in Neural Information Processing Systems, pp. 1385–1392.
  • Teh, Y. W., Jordan, M. I., Beal, M. J., and Blei, D. M. (2006), “Hierarchical Dirichlet Processes,” Journal of the American Statistical Association, 101, 1566–1581. DOI: 10.1198/016214506000000302.
  • Tyurin, I. S. (2010), “An Improvement of Upper Estimates of the Constants in the Lyapunov Theorem,” Russian Mathematical Surveys, 65, 201–202.

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