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Research Article

Sequentially allocated merge-split samplers for conjugate Bayesian nonparametric models

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Pages 1487-1511 | Received 17 Jun 2021, Accepted 19 Oct 2021, Published online: 11 Nov 2021

References

  • Ferguson TS. A Bayesian analysis of some nonparametric problems. Ann Stat. 1973;1(2):209–230.
  • Blackwell D, MacQueen JB. Ferguson distributions via Pólya urn schemes. Ann Stat. 1973;1(2):353–355.
  • Antoniak CE. Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Ann Stat. 1974;1152–1174.
  • Ferguson TS. Prior distributions on spaces of probability measures. Ann Stat. 1974;2(4):615–629.
  • Korwar RM, Hollander M. Contributions to the theory of Dirichlet processes. Ann Probab. 1973;1(4):705–711.
  • Lo AY. On a class of Bayesian nonparametric estimates: I. Density estimates. Ann Stat. 1984;12(1):351–357.
  • Pitman J. Exchangeable and partially exchangeable random partitions. Theory and Related Fields¡/DIFdel¿Probab Theory Relat Fields. 1995;102(2):145–158.
  • Ishwaran H, James LF. Gibbs sampling methods for stick-breaking priors. J Am Stat Assoc. 2001;96(453):161–173.
  • Lijoi A, Prünster I, Walker SG. Investigating nonparametric priors with Gibbs structure. Stat Sin. 2008;1653–1668.
  • Favaro S, Teh YW. MCMC for normalized random measure mixture models. Stat Sci. 2013;28(3):335–359.
  • Gelfand AE, Smith AF. Sampling-based approaches to calculating marginal densities. J Am Stat Assoc. 1990;85(410):398–409.
  • Escobar MD. Estimating normal means with a Dirichlet process prior. J Am Stat Assoc. 1994;89(425):268–277.
  • Neal RM. Connectionist learning of belief networks. Intelligence¡/DIFdel¿Artif Intell. 1992;56(1):71–113.
  • MacEachern SN. Estimating normal means with a conjugate style Dirichlet process prior. Commun Stat-Simul Comput. 1994;23(3):727–741.
  • Escobar MD, West M. Bayesian density estimation and inference using mixtures. J Am Stat Assoc. 1995;90(430):577–588.
  • MacEachern SN, Müller P. Estimating mixture of Dirichlet process models. J Comput Graph Stat. 1998;7(2):223–238.
  • Neal RM. Markov chain sampling methods for Dirichlet process mixture models. J Comput Graph Stat. 2000;9(2):249–265.
  • Fall MD, Barat É. Gibbs sampling methods for Pitman-Yor mixture models. HAL archives-ouvertes; 2014.
  • Kalli M, Griffin JE, Walker SG. Slice sampling mixture models. Stat Comput. 2011;21(1):93–105.
  • Jain S, Neal RM. A split-merge Markov chain Monte Carlo procedure for the Dirichlet process mixture model. J Comput Graph Stat. 2004;13(1):158–182.
  • Metropolis N, Rosenbluth AW, Rosenbluth MN, et al. Equation of state calculations by fast computing machines. J Chem Phys. 1953;21(6):1087–1092.
  • Hastings WK. Monte Carlo sampling methods using Markov chains and their applications. Biometrika. 1970;57(1):97–109.
  • Dahl DB. An improved merge-split sampler for conjugate Dirichlet process mixture models. Tech Rep NAVTRADEVCEN. 2003;1:086.
  • Jain S, Neal RM. Splitting and merging components of a nonconjugate Dirichlet process mixture model. Bayesian Anal.. 2007;2(3):445–472.
  • Tierney L. Markov chains for exploring posterior distributions. Ann Stat. 1994;1701–1728.
  • Green PJ, Richardson S. Modelling heterogeneity with and without the Dirichlet process. Scandinavian J Stat. 2001;28(2):355–375.
  • Dahl DB, Day R, Tsai JW. Random partition distribution indexed by pairwise information. J Am Stat Assoc. 2017;112(518):721–732.
  • Gelman A, Carlin JB, Stern HS, et al. Bayesian data analysis. Chapman and Hall/CRC; 2013.

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