Skip to main content

Exchangeability

  • Reference work entry
  • First Online:
The New Palgrave Dictionary of Economics
  • 14 Accesses

Abstract

Exchangeability is an invariance property of probability distributions that is central to the process of specifying Bayesian statistical models. Exchangeability judgements play a role in Bayesian modelling analogous to judgments in frequentist modelling that observable quantities may be regarded as realizations of independent identically distributed (IID) random variables. Judgements of conditional exchangeability (given the values of relevant covariates), when combined with Bayesian nonparametric modelling, provide a principled and rather general approach to Bayesian model specification that can lead to well-calibrated inferences and predictions; other approaches to achieving this goal include cross-validation and Bayesian model averaging.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 6,499.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 8,499.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Bibliography

  • Bernardo, J.M., and A.F.M. Smith. 1994. Bayesian theory. New York: Wiley.

    Book  Google Scholar 

  • de Finetti, B. 1930. Funzione caratteristica di un fenomeno aleatorio. Memorie della Reale Accademia dei Lincei 4: 86–133.

    Google Scholar 

  • de Finetti, B. 1937. La prévision: ses lois logiques, ses sources subjectives. Annales de l’Institut H. Poincaré 7, 1–68. Reprinted in translation as: Foresight: its logical laws, its subjective sources. In Studies in Subjective Probability, ed. H.E. Kyburg and H.E. Smokler. New York: Dover, 1980.

    Google Scholar 

  • de Finetti, B. 1938. Sur la condition d’équivalence partielle. Actualités Scientifiques et Industrielles 739. Reprinted in translation as: On the condition of partial exchangeability. In Studies in Inductive Logic and Probability, ed. R.C. Jeffrey. Berkeley: University of California Press, 1980.

    Google Scholar 

  • de Finetti, B. 1970. Teoria delle Probabilità, 2 vols. Turin: Eunaudi. Reprinted in translation as de Finetti B. 1974–75. Theory of Probability, 2 vols. Chichester: Wiley, 1974–75.

    Google Scholar 

  • Dey, D.D., P. Müller, and D. Sinha (eds.). 1998. Practical nonparametric and semiparametric Bayesian statistics. New York: Springer.

    Google Scholar 

  • Diaconis, P., and D. Freedman. 1980. Finite exchangeable sequences. Ann. Probab. 8: 745–764.

    Article  Google Scholar 

  • Draper, D. 1995. Assessment and propagation of model uncertainty (with discussion). Journal of the Royal Statistical Society: Series B 57: 45–97.

    Google Scholar 

  • Draper, D. 2007. Bayesian multilevel analysis and MCMC. In Handbook of multilevel analysis, ed. J. de Leeuw and E. Meijer. New York: Springer.

    Google Scholar 

  • Draper, D., J. Hodges, C. Mallows, and D. Pregibon. 1993. Exchangeability and data analysis (with discussion). Journal of Royal Statistics Society, Series A 156: 9–37.

    Article  Google Scholar 

  • Ferguson, T.S. 1973. A Bayesian analysis of some nonparametric problems. The Annals of Statistics 1: 209–230.

    Article  Google Scholar 

  • Fisher, R.A. 1956. Statistical methods and scientific inference. Edinburgh: Oliver and Boyd.

    Google Scholar 

  • Fréchet, M. 1943. Les Probabilités Associées à un Système d’Événements Compatibles et Dépendents, vol. 2. Paris: Hermann et Cie.

    Google Scholar 

  • Gilks, W.R., S. Richardson, and D.J. Spiegelhalter (eds.). 1995. Markov Chain Monte Carlo in practice. New York: Chapman & Hall/CRC.

    Google Scholar 

  • Good, I.J. 1950. Probability and the weighing of evidence. London: Charles Griffin.

    Google Scholar 

  • Good, I.J. 1965. The estimation of probabilities: An essay on modern Bayesian methods. Cambridge, MA: MIT Press.

    Google Scholar 

  • Haag, J. 1924. Sur un problème général de probabilités et ses diverses applications. Proceedings of the International Congress of Mathematics (Toronto) 2: 659–674.

    Google Scholar 

  • Hewitt, E., and L.J. Savage. 1955. Symmetric measures on Cartesian products. Transactions of the American Mathematical Society 80: 470–501.

    Article  Google Scholar 

  • Jaynes, E.T. 2003. Probability theory: The logic of science. Cambridge, UK: Cambridge University Press.

    Book  Google Scholar 

  • Johnson, W.E. 1924. Logic. III. The logical foundations of science. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Khintchine, A.I. 1932. Sur les classes d’événements équivalents. Mathematics of the USSR – Sbornik 39: 40–43.

    Google Scholar 

  • Lavine, M. 1992. Some aspects of Pólya tree distributions for statistical modeling. The Annals of Statistics 20: 1222–1235.

    Article  Google Scholar 

  • Leamer, E.E. 1978. Specification searches: Ad Hoc inference with nonexperimental data. New York: Wiley.

    Google Scholar 

  • Lindley, D.V., and M.R. Novick. 1981. The role of exchangeability in inference. The Annals of Statistics 9: 45–58.

    Article  Google Scholar 

  • Savage, L.J. 1954. The foundations of statistics. New York: Wiley.

    Google Scholar 

  • Stone, M. 1974. Cross-validation choice and assessment of statistical predictions (with discussion). Journal of the Royal Statistical Society: Series B 36: 111–147.

    Google Scholar 

  • Tukey, J.W. 1962. The future of data analysis. Annals of Mathematical Statistics 33: 1–67.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Copyright information

© 2018 Macmillan Publishers Ltd.

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Draper, D. (2018). Exchangeability. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_2822

Download citation

Publish with us

Policies and ethics