Bayesian Nonparametrics took off with two papers of Ferguson (Ann Stat. 2:615–629; 1963, Bayesian density estimation by mixtures of normal distributions. In Recent advances in statistics, pp 287–302. Academic Press, New York; 1983) and followed by Antoniak (Ann. Stat. 2: 1152–1174; 1974). However consistency or asymptotics were not major issue in those papers, which were more concerned with taking the first steps towards a usable, easy to interpret prior with easy to choose hyperparameters and a rich support. Unfortunately, the fact that the Dirichlet sits on discrete distributions diminished the early enthusiasm.

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Posterior Consistency in Bayesian Nonparametrics

  • Jayanta K. Ghosh,
  • R. V. Ramamoorthi

摘要

Bayesian Nonparametrics took off with two papers of Ferguson (Ann Stat. 2:615–629; 1963, Bayesian density estimation by mixtures of normal distributions. In Recent advances in statistics, pp 287–302. Academic Press, New York; 1983) and followed by Antoniak (Ann. Stat. 2: 1152–1174; 1974). However consistency or asymptotics were not major issue in those papers, which were more concerned with taking the first steps towards a usable, easy to interpret prior with easy to choose hyperparameters and a rich support. Unfortunately, the fact that the Dirichlet sits on discrete distributions diminished the early enthusiasm.