Bayesian evidence test for precise hypotheses

Journal of Statistical Planning and Inference

Volumn 117, Issue 2, 2003, Pages 185-198

  Madruga, M R ^a   Pereira, C A B ^a   Stern, J M ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Evidence; Full Bayesian significance test; Invariant formulation; Reference density; Relative surprise; Uninformative prior

Indexed keywords

EID: 0042261527     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(02)00368-3     Document Type: Article

References (47)

1. Barlow, R., Prochan, F., 1981. Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, MD.
2. Basu, D., 1988. Statistical Information and Likelihood. In: Ghosh, J.K. (Ed.), Lecture Notes in Statistics, Vol. 45. Springer, Berlin.
3. Birnbaum A. More on concepts of statistical evidence J. Amer. Statist. Assoc. 67 1972 858-861
4. Box G.E.P. Tiao G.C. Bayesian Inference in Statistical Analysis 1973 Wiley New York
5. Carnap R. Logical Foundations of Probability 1962 University of Chicago Press Chicago
6. Cox D.R. The role of significance tests Scand. J. Statist. 4 1977 49-70
7. DeGroot M.H. Optimal Statistical Decisions 1970 McGraw-Hill New York
8. Evans M. Bayesian inference procedures derived via the concept of relative surprise Comm. Statist. 26 1997 1125-1143
9. Finetti, B. de, 1974. Theory of Probability, Vols. 1 and 2. Wiley, London.
10. Finetti, B. de, 1981/1991. Scritti, Vol. 1, 1926-1930, Vol. 2, 1931-1936. CEDAM, Padova.
11. Finetti B. de Probabilitá e Induzione 1993 CLUEB Bologna
12. Gaskins R.H. Burdens of Proof in Modern Discourse 1992 Yale University Press New Haven
13. Gentle J.E. Random Number Generation and Monte Carlo Methods 2000 Springer New York
14. Good I.J. Good Thinking: The Foundations of Probability and its Applications 1983 University of Minnesota Press Minnespotts, MN
15. Irony T.Z. Lauretto M. Pereira C.A.B. Stern J.M. A Weibull wearout test: full Bayesian approach. In: Hayakawa Y. Irony T. Xie M. (Eds.), Systems and Bayesian Reliability 2002 287-300 World Scientific Singapore
16. Kempthorne O. Of what use are tests of significance and tests of hypothesis Comm. Statist. Theory Methods 8 A5 1976 763-777
17. Kempthorne, O., 1980. Foundations of statistical thinking and reasoning. Austral. CSIRO-DMS Newslett. 68 (1-5) 69, 3-7.
18. Klein D.A. Rota G.C. Introduction to Geometric Probability 1997 Cambridge University Press Cambridge
19. Kocherlakota S. Kocherlakota K. Bivariate Discrete Distributions 1992 Marcel Decker New York
20. Kokott J. The Burden of Proof in Comparative and International Human Rights Law 1998 Kluwer The Hague
21. Lauretto, M., Pereira, C.A.B., Stern, J.M., 2002. Comparing parameters of two bivariate normal distributions using the invariant full Bayesian significance test. Seventh Valencia International Meeting on Bayesian Statistics. Abstracts, pp. 155. ISBA International Meeting, Tenerife, Canary Islands, Spain.
22. Lehmann E.L. Testing Statistical Hypothesis 1986 Wiley New York
23. Lindley D.V. A statistical paradox Biometrika 44 1957 187-192
24. Lindley D.V. The Bayesian approach Scand. J. Statist. 5 1978 1-26
25. Liu J.S. Monte Carlo Methods in Scientific Computing 2001 Springer New York
26. Ljung L. Pflug G. Walk H. Stochastic Approximation and Optimization of Random Systems 1992 Birkhäuser Basel
27. Luenberger D.G. Linear and Nonlinear Programming 1984 Addison-Wesley Reading
28. Madruga M.R. Esteves L.G. Wechsler S. On the Bayesianity of Pereira-Stern tests Test 10 2001 291-299
29. McCormick G.P. Nonlinear Programming 1983 Wiley New York
30. Montoya-Delgado L.E. Irony T.Z Pereira C.A.B. Whittle M. Unconditional exact test for the Hardy-Weinberg law Genetics 875-883 2001
31. Ökten, G., 1999. Contributions to the Theory of Monte Carlo and Quasi-Monte Carlo Methods. www:dissertation.com
32. Paul S.R. Ho N.I. Estimation in the Biavariate Poisson Distribution and Hypothesis Testing Concerning Independence Communications in Statistics-Theory and Methods 18 1989 1123-1133
33. Pereira C.A.B. Rogatko A. The Hardy-Weinberg equilibrium under a Bayesian perspective Braz. J. Genetics 7 1984 689-707
34. Pereira, C.A.B., Stern, J.M., 1999a. A Dynamic Software Certification and Verification Procedure. Proc. ISAS-99-International Conference on Information Systems Analysis and Synthesis II, ISAS, Orlando, FL, USA 426-435.
35. Pereira C.A.B. Stern J.M. Evidence and credibility: full Bayesian significance test for precise hypotheses Entropy 1 1999 69-80
36. Pereira C.A.B. Stern J.M. Model selection: full Bayesian approach Environmetrics 12 6 2001 559-568
37. Pereira C.A.B. Wechsler S. On the concept of p-value Braz. J. Probab. Statist. 7 1993 159-177
38. Pflug G.C. Optimization of Stochastic Models: The interface Between Simulation and Optimization 1999 Kluwer Dordrecht
39. Popper K.R. Conjectures and Refutations: The Growth of Scientific Knowledge 1989 Routledge London
40. Royall R. Statistical Evidence: A Likelihood Paradigm 1997 Chapman & Hall London
41. Rubin H. A weak system of axioms for "Rational" behaviour and the non-separability of utility from prior Statist. Decisions 5 1987 47-58
42. Santalo L.A. Integral Geometry and Geometric Probability Encyclopedia of Mathematics and its Applications Vol. 1 1976 Addison-Wesley London
43. Savage L.J. The Foundations of Statistical Inference 1962 Methuen London
44. Sellke, T., Bayarri, M.J., Berger, J., 1999. Calibration of p-values for testing precise null hypotheses. ISDS Discussion Paper 99-13.
45. Spall J.C. Adaptive stochastic approximation by the simultaneous perturbation method IEEE Trans. Automat. Control 45 2000 1839-1853
46. Stern, J.S., Zacks, S., 2002. Testing the independence of poisson variates under the Holgate bivariate distribution The power of a new evidence test. RT-MAC-IME-USP 2002-03. Tech. Rep. Univ. of São Paulo. Submitted, Statistics and Probability Letters.
47. Zellner A. An Introduction to Bayesian Inference in Econometrics 1971 Wiley New York