The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Bayesian Non-parametrics

  • Stephen Graham Walker
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_2596

Abstract

This article discusses Bayesian nonparametric models, arguing that all Bayesians are constructing probability distributions (the prior) on spaces of density functions. The parametric Bayesian can be seen to be making restrictive assumptions about the choice of density for modelling data. In contrast, the nonparametric Bayesian constructs a probability distribution on as many densities as possible. The model is infinite dimensional, yet inference is possible, including density estimation and the implementation of decision rules, such as the maximization of expected utility. An example of a nonparametric model is given and a means by which to make inference provided by simulation techniques.

Keywords

Bayesian nonparametrics Density functions Expected utility Latent variables Likelihood Markov chain Monte Carlo methods Parametric models Probability distribution Statistical inference Uncertainty 

JEL Classifications

C11 C14 
This is a preview of subscription content, log in to check access.

Bibliography

  1. Bernardo, J.M., and A.F.M. Smith. 1994. Bayesian theory. London: Wiley.CrossRefGoogle Scholar
  2. Escobar, M.D. 1988. Estimating the means of several normal populations by nonparametric estimation of the distribution of the means. Ph.D. thesis, Department of Statistics, Yale University.Google Scholar
  3. Ferguson, T.S. 1973. A Bayesian analysis of some nonparametric problems. Annals of Statistics 1: 209–230.CrossRefGoogle Scholar
  4. Hirshleifer, J., and J.G. Riley. 1992. The analysis of uncertainty and information. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  5. Lindley, D.V. 1978. The Bayesian approach (with discussion). Scandinavian Journal of Statistics 5: 1–26.Google Scholar
  6. Lindsey, J.K. 1999. Some statistical heresies. The Statistician 48: 1–40.Google Scholar
  7. Lo, A.Y. 1984. On a class of Bayesian nonparametric estimates I Density estimates. Annals of Statistics 12: 351–357.CrossRefGoogle Scholar
  8. Smith, A.F.M., and G.O. Roberts. 1993. Bayesian computations via the Gibbs sampler and related Markov chain Monte Carlo methods. Journal of the Royal Statistical Society, Series B 55: 3–23.Google Scholar
  9. Tierney, L. 1994. Markov chains for exploring posterior distributions. Annals of Statistics 22: 1701–1722.CrossRefGoogle Scholar
  10. Walker, S.G., P. Damien, P.W. Laud, and A.F.M. Smith. 1999. Bayesian nonparametric inference for random distributions and related functions (with discussion). Journal of the Royal Statistical Society, Series B 61: 485–527.CrossRefGoogle Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Stephen Graham Walker
    • 1
  1. 1.