Skip to main content
SpringerLink
Log in

Bayesian Statistics

  • Reference work entry
  • First Online:
Book cover International Encyclopedia of Statistical Science

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 1,100.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
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

References and Further Reading

  • Bartlett M (1957) A comment on D.V. Lindley’s statistical paradox. Biometrika 44:533–534

    MATH  MathSciNet  Google Scholar 

  • Berger JO (1985) Statistical decision theory and Bayesian analysis. Springer, Berlin

    MATH  Google Scholar 

  • Berger JO (2000) Bayesian analysis: a look at today and thoughts of tomorrow. J Am Stat Assoc 95:1269–1276

    MATH  Google Scholar 

  • Berger JO, Bernardo JM (1989) Estimating a product of means: Bayesian analysis with reference priors. J Am Stat Assoc 84:200–207

    MATH  MathSciNet  Google Scholar 

  • Berger JO, Bernardo JM (1992) On the development of reference priors. In: Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds) Bayesian statistics, vol 4. Oxford University Press, Oxford, pp 35–60 (with discussion)

    Google Scholar 

  • Berger J, Bernardo JM, Sun D (2009a) The formal definition of reference priors. Ann Stat 37:905–938

    MATH  MathSciNet  Google Scholar 

  • Berger JO, Bernardo JM, Sun D (2009b) Natural induction: an objective Bayesian approach. Rev Acad Sci Madrid A 103:125–159 (with discussion)

    Google Scholar 

  • Bernardo JM (1979a) Expected information as expected utility. Ann Stat 7:686–690

    MATH  MathSciNet  Google Scholar 

  • Bernardo JM (1979b) Reference posterior distributions for Bayesian inference. J R Stat Soc B 41: 113–147 (with discussion). In: Tiao GC, Polson GC (eds) Reprinted in Bayesian Inference 1. Edward Elgar, Oxford, pp 229–263

    Google Scholar 

  • Bernardo JM (1997) Noninformative priors do not exist. J Stat Plann Infer 65:159–189 (with discussion)

    Google Scholar 

  • Bernardo JM (2005a) Reference analysis. In: Dey DK, Rao CR (eds) Handbook of Statistics, vol 25. Elsevier, Amsterdam, pp 17–90

    Google Scholar 

  • Bernardo JM (2005b) Intrinsic credible regions: An objective Bayesian approach to interval estimation. Test 14:317–384 (with discussion)

    Google Scholar 

  • Bernardo JM (2010) Integrated objective Bayesian estimation and hypothesis testing. In: Bernardo JM et al. (eds) Bayesian Statistics 9. Oxford: Oxford University Press, (to appear, with discussion)

    Google Scholar 

  • Bernardo JM, Ramón JM (1998) An introduction to Bayesian reference analysis: inference on the ratio of multinomial parameters. The Statistician 47:1–35

    Google Scholar 

  • Bernardo JM, Rueda R (2002) Bayesian hypothesis testing: a reference approach. Int Stat Rev 70:351–372

    MATH  Google Scholar 

  • Bernardo JM, Smith AFM (1994) Bayesian theory. Wiley, Chichester

    MATH  Google Scholar 

  • Bernardo JM, Bayarri MJ, Berger JO, Dawid AP, Heckerman D, Smith AFM, West M (eds) (2003) Bayesian statistics 7. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Bernardo JM, Bayarri MJ, Berger JO, Dawid AP, Heckerman D, Smith AFM, West M (eds) (2007) Bayesian statistics 8. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Berry DA (1996) Statistics, a Bayesian perspective. Wadsworth, Belmont

    Google Scholar 

  • Box GEP, Tiao GC (1973) Bayesian inference in statistical analysis. Addison-Wesley, Reading

    MATH  Google Scholar 

  • Dawid AP, Stone M, Zidek JV (1973) Marginalization paradoxes in Bayesian and structural inference. J R Stat Soc B 35:189–233 (with discussion)

    Google Scholar 

  • de Finetti B (1970) Teoria delle Probabilità. Einaudi, Turin. English translation: Theory of Probability (1975) Wiley, Chichester

    Google Scholar 

  • DeGroot MH (1970) Optimal statistical decisions. McGraw-Hill, New York

    MATH  Google Scholar 

  • de Finetti B (1937) La prvision, ses lois logiques, ser sources sunjecives. Ann Inst Henri Poincaré 7:1–68

    Google Scholar 

  • Efron B (1986) Why isn’t everyone a Bayesian? Am Stat 40:1–11 (with discussion)

    Google Scholar 

  • Geisser S (1993) Predictive inference: an introduction. Chapman and Hall, London

    MATH  Google Scholar 

  • Gelfand AE, Smith AFM (1990) Sampling based approaches to calculating marginal densities. J Am Stat Assoc 85: 398–409

    MATH  MathSciNet  Google Scholar 

  • Gelman A, Carlin JB, Stern H, Rubin DB (1995) Bayesian data analysis. Chapman and Hall, London

    Google Scholar 

  • Gilks WR, Richardson S, Spiegelhalter DJ (1996) Markov chain Monte Carlo in practice. Chapman and Hall, London

    MATH  Google Scholar 

  • Jaynes ET (1976) Confidence intervals vs Bayesian intervals. In: Harper WL, Hooker CA (eds) Foundations of probability theory, statistical inference and statistical theories of science, vol 2. Reidel, Dordrecht, pp 175–257 (with discussion)

    Google Scholar 

  • Jeffreys H (1961) Theory of probability, 3rd edn. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Kass RE, Raftery AE (1995) Bayes factors. J Am Stat Assoc 90: 773–795

    MATH  Google Scholar 

  • Laplace PS (1812) Théorie Analitique des Probabilités. Paris: Gauthier-Villars

    Google Scholar 

  • Lindley DV (1957) A statistical paradox. Biometrika 44:187–192

    MATH  MathSciNet  Google Scholar 

  • Lindley DV (1958) Fiducial distribution and Bayes theorem. J R Stat Soc B 20:102–107

    MATH  MathSciNet  Google Scholar 

  • Lindley DV (1965) Introduction to probability and statistics from a Bayesian viewpoint. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Lindley DV (1972) Bayesian Statistics, a review. SIAM, Philadelphia

    Google Scholar 

  • Lindley DV (1985) Making Decisions, 2nd edn. Wiley, Chichester

    Google Scholar 

  • Lindley DV (2000) The philosophy of statistics. The Statistician 49:293–337 (with discussion)

    Google Scholar 

  • O’Hagan A (1994) Bayesian Inference. Edward Arnold, London

    MATH  Google Scholar 

  • Press SJ (1972) Applied multivariate analysis: using Bayesian and frequentist methods of inference. Krieger, Melbourne

    Google Scholar 

  • Ramsey FP (1931) Truth and probability. In: Braithwaite RB (ed) The foundations of mathematics and other logical essays. London: Kegan Paul, pp 156–198

    Google Scholar 

  • Wald A (1950) Statistical decision functions. Wiley, Chichester

    MATH  Google Scholar 

  • West M, Harrison PJ (1989) Bayesian forecasting and dynamic models. Springer, Berlin

    MATH  Google Scholar 

  • Zellner A (1971) An introduction to Bayesian inference in econometrics. Wiley, New York. Reprinted in 1987, Krieger, Melbourne

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universitat de València, Burjassot, Spain

    José M. Bernardo (Professor of Statistics, Facultad de Matemáticas)

Authors
  1. José M. Bernardo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac, City of Kragujevac, Serbia

    Miodrag Lovric

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this entry

Cite this entry

Bernardo, J.M. (2011). Bayesian Statistics. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_139

Download citation

Publish with us

Policies and ethics

Search

Navigation