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Basic Fiducial Bayesian Procedures for Inference About Means

  • Bruno Lecoutre
  • Jacques Poitevineau
Chapter
Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)

Abstract

This chapter presents the basic fiducial Bayesian procedures for a contrast between means, which is an issue of particular importance for experimental data analysis. The presentation is essentially non-technical. Focus is on the computational and methodological aspects.

Keywords

A Bayesian alternative to frequentist procedures Basic fiducial Bayesian procedures Bayesian interpretation of p-values and confidence levels Inference about a difference between means LePAC statistical inference package Specific inference  

References

  1. Fisher, R.A.: Statistical methods and scientific inference (reprinted 3rd edition, 1973). In: Bennett, J.H. (ed.) Statistical Methods, Experimental Design, and Scientific Inference. Oxford University Press, Oxford (1990c)Google Scholar
  2. Gertsbakh, I., Winterbottom, A.: 1991: Point and interval estimation of normal tail probabilities. Commun. Stat. A-Theor 20, 1497–1514 (1991)CrossRefMathSciNetGoogle Scholar
  3. Lecoutre, B.: Bayesian predictive procedure for designing and monitoring experiments. Bayesian Methods with Applications to Science. Policy and Official Statistics, pp. 301–310. Office for Official Publications of the European Communities, Luxembourg (2001)Google Scholar
  4. Lecoutre, B.: Traitement statistique des données expérimentales: des pratiques traditionnelles aux pratiques bayésiennes. SPAD, Suresnes, FR (1996). Bayesian Windows programs by B. Lecoutre and J. Poitevineau, http://www.univ-rouen.fr/LMRS/Persopage/Lecoutre/Eris Cited 13 March 2014
  5. Lecoutre, B.: Extensions de l’analyse de la variance: L’analyse bayésienne des comparaisons. Math. Sci. Hum. 75, 49–69 (1981)zbMATHMathSciNetGoogle Scholar
  6. Lecoutre, B.: L’Analyse Bayésienne Des Comparaisons. Presses Universitaires de Lille, Lille (1984)Google Scholar
  7. Lecoutre, B., Derzko, G., Grouin, J.-M.: Bayesian predictive approach for inference about proportions. Stat. Med. 14, 1057–1063 (1995)CrossRefGoogle Scholar
  8. Lecoutre, B.: Two useful distributions for Bayesian predictive procedures under normal models. J. Stat. Plan. Infer. 79, 93–105 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  9. Lecoutre, B., Mabika, B., Derzko, G.: Assessment and monitoring in clinical trials when survival curves have distinct shapes in two groups: A Bayesian approach with Weibull modeling. Stat. Med. 21, 663–674 (2002)CrossRefGoogle Scholar
  10. Lecoutre, B.: Training students and researchers in Bayesian methods. J. Data Sci. 4, 207–232 (2006)Google Scholar
  11. Lecoutre, B.: Another look at confidence intervals for the noncentral t distribution. J. Mod. Appl. Stat. Methods 6, 107–116 (2007)Google Scholar
  12. Lecoutre, B.: Bayesian methods for experimental data analysis. In: Rao, C.R., Miller, J., Rao, D.C. (eds.) Handbook of statistics: Epidemiology and Medical Statistics (Vol 27), pp. 775–812. Elsevier, Amsterdam (2008)Google Scholar
  13. Poitevineau, J., Lecoutre, B.: Implementing Bayesian predictive procedures: the K-prime and K-square distributions. Comput. Stat. Data An. 54, 723–730 (2010)CrossRefMathSciNetGoogle Scholar
  14. Rouanet, H., Lecoutre, B.: Specific inference in ANOVA: from significance tests to Bayesian procedures. Brit. J. Math. Stat. Psy. 36, 252–268 (1983)CrossRefzbMATHGoogle Scholar
  15. Rouanet, H.: Bayesian procedures for assessing importance of effects. Psychol. Bull. 119, 149–158 (1996)CrossRefGoogle Scholar
  16. Le Roux, B., Rouanet, H.: Geometric Data Analysis: From Correspondence Analysis to Structured Data Analysis. Kluwer Academic Publisher, New York (2004)Google Scholar
  17. Thompson, B.: What future quantitative social science research could look like: confidence intervals for effect sizes. Educ. Researcher 31, 24–31 (2002)CrossRefGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.ERIS, Laboratoire de Mathématiques Raphaël SalemUMR 6085, CNRS Université de RouenSaint-Étienne-du-RouvrayFrance
  2. 2.ERIS, IJLRA UMR-7190, CNRSUniversité Pierre et Marie CurieParisFrance

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