References
- Aldous, D. (1985), “Exchangeability and Related Topics,” in École d’Été de Probabilités de Saint-Flour XIII–1983, Berlin: Springer, pp. 1–198.
- Barrios, E., Lijoi, A., Nieto-Barajas, L. E., and Prüenster, I. (2013), “Modeling With Normalized Random Measure Mixture Models,” Statistical Science, 28, 283–464.
- Blackwell, D., and McQueen, J. B. (1973), “Ferguson Distributions via Pólya urn Schemes,” Annals of Statistics, 1, 353–355.
- De Blasi, P., Favaro, S., Lijoi, A., Mena, R. H., Prüenster, I., and Ruggiero, M. (2015), “Are Gibbs-Type Priors the Most Natural Generalization of the Dirichlet Process?” IEEE Transactions on Pattern Analysis & Machine Intelligence, 37, 212–229.
- de la Mata-Espinosa, P., Bosque-Sendra, J. M., Bro, R., and Cuadros-Rodriguez, L. (2011), “Discriminating Olive and Non-Olive Oils Using HPLC-CAD and Chemometrics,” Analytical and Bioanalytical Chemistry, 399, 2083–2092.
- Devroye, L. (2009), “Random Variate Generation for Exponentially and Polynomially Tilted Stable Distributions,” ACM Transactions on Modelling and Computer Simulation, 19, 1–20.
- Escobar, M. D. (1994), “Estimating Normal Means With a Dirichlet Process Prior,” Journal of the American Statistical Association, 89, 268–277.
- Escobar, M. D., and West, M. (1995), “Bayesian Density Estimation and Inference Using Mixtures,” Journal of the American Statistical Association, 90, 577–588.
- Ewens, W. J. (1972), “The Sampling Theory of Selectively Neutral Alleles,” Theoretical Population Biology, 3, 87–112.
- Favaro, S., Lomeli, M., and Teh, Y. W. (2014), “On a Class of σ-Stable Poisson-Kingman Models and an Effective Marginalized Sampler,” Statistics and Computing, 25, 67–78.
- Favaro, S., and Teh, Y. W. (2013), “MCMC for Normalized Random Measure Mixture Models,” Statistical Science, 28, 335–359.
- Favaro, S., and Walker, S. G. (2012), “Slice Sampling σ-STable Poisson-Kingman Mixture Models,” Journal of Computational and Graphical Statistics, 22, 830–847.
- Ferguson, T. S. (1973), “A Bayesian Analysis of Some Nonparametric Problems,” Annals of Statistics, 1, 209–230.
- Gelman, A., Carlin, J., Stern, H., and Rubin, D. (1995), Bayesian Data Analysis, London: Chapman & Hall.
- Gnedin, A., and Pitman, J. (2006), “Exchangeable Gibbs Partitions and Stirling Triangles,” Journal of Mathematical Sciences, 138, 5674–5684.
- Griffin, J. E., and Walker, S. G. (2011), “Posterior Simulation of Normalized Random Measure Mixtures,” Journal of Computational and Graphical Statistics, 20, 241–259.
- Ho, M. W., James, L. F., and Lau, J. W. (2008), “Gibbs Partitions (EPPFs) Derived From a Stable Subordinator are Fox H and Meijer G Transforms,” ArXiv:0708.0619.
- Ishwaran, H., and James, L. F. (2001), “Gibbs Sampling Methods for Stick-Breaking Priors,” Journal of the American Statistical Association, 96, 161–173.
- James, L. F. (2002), “Poisson Process Partition Calculus With Applications to Exchangeable Models and Bayesian Nonparametrics,” ArXiv:math/0205093.
- ——— (2013), “Stick-Breaking PG(α, ψ)-Generalized Gamma Processes,” ArXiv:1308.6570.
- James, L. F., Lijoi, A., and Prüenster, I. (2009), “Posterior Analysis for Normalized Random Measures With Independent Increments,” Scandinavian Journal of Statistics, 36, 76–97.
- Jolliffe, I. (2002), Principal Component Analysis (2nd ed.), Berlin: Springer Verlag.
- Kalli, M., Griffin, J. E., and Walker, S. G. (2011), “Slice Sampling Mixture Models,” Statistics and Computing, 21, 93–105.
- Kanter, M. (1975), “Stable Densities Under Change of Scale and Total Variation Inequalities,” Annals of Probability, 3, 697–707.
- Kingman, J. F. C. (1967), “Completely Random Measures,” Pacific Journal of Mathematics, 21, 59–78.
- ——— (1975), “Random Discrete Distributions, Journal of the Royal Statistical Society, Series B, 37, 1–22.
- ——— (1978), “The Representation of Partition Structures,” Journal of the London Mathematical Society, 18, 374–380.
- Lijoi, A., Mena, R. H., and Prüenster, I. (2005), “Hierarchical Mixture Modelling With Normalized Inverse-Gaussian Priors,” Journal of the American Statistical Association, 100, 1278–1291.
- ——— (2007), “Controlling the Reinforcement in Bayesian Nonparametric Mixture Models, Journal of the Royal Statistical Society, Series B, 69, 715–740.
- Lijoi, A., Prünster, I., and Walker, S. G. (2008), “Investigating Nonparametric Priors With Gibbs Structure,” Statistica Sinica, 18, 1653–1668.
- Lo, A. (1984), “On a Class of Bayesian Nonparametric Estimates: I. Density Estimates,” Annals of Statistics, 12, 351–357.
- MacEachern, S. N. (1994), “Estimating Normal Means With a Conjugate Style Dirichlet Process Prior,” Communications in Statistics: Simulation and Computation, 23, 727–741.
- Medvedovic, M., and Sivaganesan, S. (2002), “Bayesian Infinite Mixture Model Based Clustering of Gene Expression Profiles,” Bioinformatics, 18, 1194–1206.
- Miller, J. W., and Harrison, T. M. (2013), “A Simple Example of Dirichlet Process Mixture Inconsistency for the Number of Components,” in Neural Information Processing Systems.
- Neal, R. M. (2000), “Markov Chain Sampling Methods for Dirichlet Process Mixture Models,” Journal of Computational and Graphical Statistics, 9, 249–265.
- ——— (2003), “Slice Sampling,” Annals of Statistics, 31, 705–767.
- Nieto-Barajas, L. E., Pruenster, I., and Walker, S. G. (2004), “Normalized Random Measures Driven by Increasing Additive Processes,” Annals of Statistics, 32, 2343–2360.
- Papaspiliopoulos, O., and Roberts, G. O. (2008), “Retrospective Markov Chain Monte Carlo Methods for Dirichlet Process Hierarchical Models,” Biometrika, 95, 169–186.
- Perman, M., Pitman, J., and Yor, M. (1992), “Size-Biased Sampling of Poisson Point Processes and Excursions,” Probability Theory and Related Fields, 92, 21–39.
- Pitman, J. (2003), “Poisson-Kingman Partitions,” in Statistics and Science: a Festschrift for Terry Speed, ed. D. R. Goldstein, Shaker Heights, OH: Institute of Mathematical Statistics, pp. 1–34.
- ——— (2006), Combinatorial Stochastic Processes, Lecture Notes in Mathematics, Berlin: Springer-Verlag.
- Pitman, J., and Yor, M. (1997), “The Two Parameter Poisson-Dirichlet Distribution Derived From a Stable Subordinator,” Annals of Probability, 25, 855–900.
- Regazzini, E., Lijoi, A., and Prüenster, I. (2003), “Distributional Results for Means of Random Measures With Independent Increments,” Annals of Statistics, 31, 560–585.
- Roeder, K. (1990), “Density Estimation With Confidence Sets Exemplified by Super-Clusters and Voids in the Galaxies,” Journal of the American Statistical Association, 85, 617–624.
- Tanner, M., and Wong, W. (1987), “The Calculation of Posterior Distributions by Data Augmentation,” Journal of the American Statistical Association, 82, 528–550.
- Walker, S. G. (2007), “Sampling the Dirichlet Mixture Model With Slices,” Communications in Statistics—Simulation and Computation, 36, 45–54.
- Wuertz, A., Maechler, M., and Rmetrics Core Team Members (2013), Stabledist. CRAN R Package Documentation.
- Zolotarev, V. M. (1966), “On the Representation of Stable Laws by Integrals,” Selected Translations Mathematical Statistics and Probability, 6, 84–88.