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Bibliography J. D. McAuliffe, D. M. Blei, and M. I. Jordan. Nonparametric empirical Bayes for the Dirichlet process mixture model. Statisitcs and Computing, 16:5–14, 2006. D. McFadden. Economic choice. In T. Persson, editor, Nobel Lectures, Economics 1996-2000, pages 330–364. World Scientific Publishing, 2000. B. L. McNaughton, J. O’Keffe, and C. A. Barnes. The stereotrode - a new technique for simultaneous isolation of several single units in the central nervous-system from multiple unit records. Journal of Neuroscience Methods, 8(4):391–397, 1983. E. Meeds and S. Osindero. An alternative infinite mixture of gaussian process experts. In Y. Weiss, B. Schölkopf, and J. Platt, editors, Advances in Neural Information Processing Systems, volume 18, pages 883–890. MIT Press, Cambridge, MA, 2006. E. Meeds, Z. Ghahramani, R. M. Neal, and S. T. Roweis. Modeling dyadic data with binary latent factors. In B. Sch ´ ’olkopf, J. Platt, and T. Hofmann, editors, Advances in Neural Information Processing Systems, volume 19. MIT Press, 2007. T. Minka and Z. Ghahramani. Expectation propagation for infinite mixtures. In NIPS Workshop on Nonparametric Bayesian Methods and Infinite Models, 2003. P. Muliere and L. Tardella. Approximating distributions of random functionals of Ferguson-Dirichlet priors. The Canadian Journal of Statistics, 26(2):283–297, 1998. P. Müller and F. A. Quintana. Nonparametric Bayesian data analysis. Statistical Science, 19(1):95–110, 2004. D. Navarro and T. L. Griffiths. A nonparametric Bayesian method for inferring features from similarity judgment. In B. Sch ´ ’olkopf, J. Platt, and T. Hofmann, editors, Advances in Neural Information Processing Systems, volume 19. MIT Press, 2007. D. J. Navarro, T. L. Griffiths, M. Steyvers, and M. D. Lee. Modeling individual differences using Dirichlet processes. Journal of Mathematical Psychology, 50:101–122, 2006. R. M. Neal. Markov chain sampling methods for Dirichlet process mixture models. Journal of Computational and Graphical Statistics, 9:249–265, 2000. R. M. Neal. Defining priors for distributions using Dirichlet diffusion trees. Technical report, University of Toronto, 2001. Apperaed in Valencia. R. M. Neal. Slice sampling. The Annals of Statistics, 31(3):705–767, 2003. R. M. Neal. Bayesian mixture modeling. In C. R. Smith, G. J. Erickson, and P. O. Neudorfer, editors, Maximum Entropy and Bayesian Methods: Proceedings of the 11th International Workshop on Maximum Entropy and Bayesian Methods of Statistical Analysis, pages 197–211. Dordrecht: Kluwer Academic Publishers, 1992. 130
Bibliography R. M. Neal. Probabilistic inference using Markov chain Monte Carlo methods. Technical report, Department of Statistics, University of Toronto, 1993. R. M. Neal. Bayesian Learning for Neural Networks. Number 118 in Lecture Notes in Statistics. Springer-Verlag, 1996. M. A. Newton and Y. Zhang. A recursive algorithm for nonparametric analysis with missing data. Biometrika, 86:15–26, 1999. D. P. Nguyen, L. M. Frank, and E. N. Brown. An application of reversible-jump Markov chain Monte Carlo to spike classification of multi-unit extracellular recordings. Network: Computation in Neural Systems, 14:61–82, 2003. A. O’Hagan. Advanced Theory of Statistics: Bayesian Inference v. 2B (Kendall’s Advanced Statistics Library). Hodder Arnold, 1994. O. Papaspiliopoulos and G. O. Roberts. Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models. submitted, 2005. S. Petrone and A. E. Raftery. A note on the Dirichlet porcess prior in Bayesian nonparametric inference with partial exchangeability. Statistics & Probability Letters, 36: 69–83, 1997. J. Pitman. Combinatorial Stochastic Processes Ecole d’Eté de Probabilités de Saint- Flour XXXII – 2002, volume 1875 of Lecture Notes in Mathematics. Springer, 2006. J. Pitman. Some developments of the Blackwell-MacQueen urn scheme. In T. S. Ferguson, L. S. Shapley, and J. B. MacQueen, editors, Statistics, Probability and Game Theory; Papers in honor of David Blackwell, volume 30 of Lecture Notes-Monograph Series, pages 245–267. Institute of Mathematical Statistics, Hayward, CA, 1996. J. Pitman and M. Yor. The two-parameter Poisson–Dirichlet distribution derived from a stable subordinator. The Annals of Probability, 25(2):855–900, 1997. I. Porteus, A. Ihler, P. Smyth, and M. Welling. Gibbs sampling for (coupled) infinite mixture models in the stick-breaking representation. In Proceedings of UAI, volume 22, 2006. F. A. Quintana. Nonparametric bayesian analysis for assessing homogeneity in k × i contingency tables with fixed right margin totals. Journal of the American Statistical Association, 93(443):1140–1149, 1998. C. E. Rasmussen. The infinite Gaussian mixture model. In S. A. Solla, T. K. Leen, and K. R. Müller, editors, Advances in Neural Information Processing Systems, volume 12, pages 554–560. MIT Press, 2000. C. E. Rasmussen and Z. Ghahramani. Infinite mixtures of gaussian process experts. In T. G. Dietterich, S. Becker, and Z. Ghahramani, editors, Advances in Neural Information Processing Systems, volume 14. MIT Press, 2002. 131
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Nonparametric Bayesian Discrete Lat
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Matrizen mit unendlich vielen Spalt
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Contents Zusammenfassung iii Abstra
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List of Algorithms 1 Gibbs sampling
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Notation Matrices are capitalized a
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Symbol Meaning IBP Z binary latent
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1 Introduction belief in the prior.
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2 Nonparametric Bayesian Analysis b
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2 Nonparametric Bayesian Analysis s
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3 Dirichlet Process Mixture Models
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3.1 The Dirichlet Process the perfo
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α G o G θi x i N 3.1 The Dirichle
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15 10 5 −0.5 0 0.5 2 1 G 0 0 −0
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increment process with the correspo
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α G o π k c i θk x i 8 N 3.1 The
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3.1 The Dirichlet Process Eq. (3.21
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number of components, K number of c
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3.2 MCMC Inference in Dirichlet Pro
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and Bush and MacEachern (1996). 3.2
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3.2.2 Algorithms for non-Conjugate
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∗ π ∗ π s 3.2 MCMC Inference
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model can be written in the form of
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−1 µ y Σy Σy D ξ normal R 3.3
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the log likelihood term is: where a
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3.3 Empirical Study on the Choice o
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autocovariance coefficient 1 0.8 0.
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# of data points # of data points 5
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3.4 Dirichlet Process Mixtures of F
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µ y Σy ξ R 0 ν w normal µ −1
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ch1 ch2 ch3 ch4 3.4 Dirichlet Proce
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3.4 Dirichlet Process Mixtures of F
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# of components # of components # o
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ch 2 ch 3 ch 1 ch 2 ch 3 ch 4 3.4 D
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3.5 Discussion 3.5 Discussion In th
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4 Indian Buffet Process Models matr
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4 Indian Buffet Process Models In t
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4 Indian Buffet Process Models α z
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4 Indian Buffet Process Models α
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4 Indian Buffet Process Models The
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4 Indian Buffet Process Models colu
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Page 104 and 105: 4 Indian Buffet Process Models rati
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Page 108 and 109: 4 Indian Buffet Process Models samp
Page 110 and 111: 4 Indian Buffet Process Models feat
Page 112 and 113: 4 Indian Buffet Process Models Algo
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Page 116 and 117: 4 Indian Buffet Process Models Figu
Page 118 and 119: 4 Indian Buffet Process Models pres
Page 120 and 121: 4 Indian Buffet Process Models ε
Page 122 and 123: 4 Indian Buffet Process Models LL P
Page 124 and 125: 4 Indian Buffet Process Models P+ P
Page 126 and 127: 4 Indian Buffet Process Models tEBA
Page 128 and 129: 4 Indian Buffet Process Models dist
Page 130 and 131: 5 Conclusions has been defined as a
Page 132 and 133: A Details of Derivations for the St
Page 135 and 136: B Mathematical Appendix B.1 Dirichl
Page 137 and 138: p3 α 1 0.5 0 0 0.5 0.4 0.3 0.2 0.1
Page 139 and 140: Construction of A Process B.4 Equal
Page 141 and 142: Bibliography D. Aldous. Exchangeabi
Page 143 and 144: Bibliography T. S. Ferguson. Prior
Page 145: Bibliography L. F. James and J. W.
Page 149 and 150: Bibliography Y. W. Teh, M. I. Jorda
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