Asymptotics for constrained dirichlet distributions

Charles Geyer, Glen Meeden

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We derive the asymptotic approximation for the posterior distribution when the data are multinomial and the prior is Dirichlet conditioned on satisfying a finite set of linear equality and inequality constraints so the posterior is also Dirichlet conditioned on satisfying these same constraints. When only equality constraints are imposed, the asymptotic approximation is normal. Otherwise it is normal conditioned on satisfying the inequality constraints. In both cases the posterior is a root-n-consistent estimator of the parameter vector of the multinomial distribution. As an application we consider the constrained Polya posterior which is a non-informative stepwise Bayes posterior for finite population sampling which incorporates prior information involving auxiliary variables. The constrained Polya posterior is a root-n-consistent estimator of the population distribution, hence yields a root-n-consistent estimator of the population mean or any other differentiable function of the vector of population probabilities.

Original languageEnglish (US)
Pages (from-to)89-110
Number of pages22
JournalBayesian Analysis
Volume8
Issue number1
DOIs
StatePublished - 2013

Keywords

  • Bayesian inference
  • Consistency
  • Constraints
  • Dirichlet distribution
  • Polya posterior
  • Sample survey

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