Bayesian Nonparametric Bootstrap Confidence Intervals

Abstract

Let X sub 1,...,X sub n be a random sample from an unknown probability distribution P on the sample space X, and let theta = theta(P) be a parameter of interest. This paper gives a Bayesian botstrap method of obtaining Bayes estimates and Bayesian confidence limits for theta, using a (non- degenerate) Dirichlet process prior for P. This extends methods and results of Rubin (1981) and Efron (1982), in that they assume the sample space to be finite and use only a particular degenerate Dirichlet prior. An asymptotic justification of the Bayesian bootstrap is given, parallelling results of Bickel and Freedman(1981). Keywords: Charts; Approximation(mathematics); Asymptotic theory.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1985
Accession Number
ADA161786

Entities

People

  • Nils L. Hjort

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Bayes Theorem
  • Confidence Limits
  • Data Science
  • Information Science
  • Intervals
  • Mathematical Analysis
  • Mathematics
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Samples
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Information Retrieval
  • AI & ML - Machine Learning Algorithms
  • Space