A WEIBULL WEAROUT TEST: FULL BAYESIAN APPROACH

The Full Bayesian Signi cance Test (FBST) for precise hypotheses is presented, with some applications relevant to reliability theory. The FBST is an alternative to signi cance tests or, equivalently, to p-values. In the FBST we compute the evidence of the precise hypothesis. This evidence is the probability of the complement of a credible set \tangent" to the sub-manifold (of the parameter space) that de nes the null hypothesis. We use the FBST in an application requiring a quality control of used components, based on remaining life statistics.

[1]  I. Good.  Good Thinking: The Foundations of Probability and Its Applications , 1983 .

[2]  Michael Evans,et al.  Bayesian ikference procedures derived via the concept of relative surprise , 1997 .

[3]  Carlos Alberto de Bragança Pereira,et al.  Model selection: Full Bayesian approach , 2001 .

[4]  M. J. Bayarri,et al.  Calibration of ρ Values for Testing Precise Null Hypotheses , 2001 .

[5]  K. B. Oldham,et al.  An Atlas of Functions. , 1988 .

[6]  D. V. Lindley,et al.  Examples Questioning the Use of Partial Likelihood , 1987 .

[7]  T. Louis,et al.  Unified frequentist and Bayesian testing of a precise hypothesis , 1997 .

[8]  V. Vieland,et al.  Statistical Evidence: A Likelihood Paradigm , 1998 .

[9]  I. Sloan.  Lattice Methods for Multiple Integration , 1994 .

[10]  Oscar Kempthorne,et al.  Probability, Statistics, and data analysis , 1973 .

[11]  Paul Bratley,et al.  A guide to simulation , 1983 .

[12]  Richard E. Barlow,et al.  Statistical Theory of Reliability and Life Testing: Probability Models , 1976 .

[13]  Rubin Herman,et al.  A WEAK SYSTEM OF AXIOMS FOR "RATIONAL" BEHAVIOR AND THE NONSEPARABILITY OF UTILITY FROM PRIOR , 1987 .

[14]  Donald E. Knuth,et al.  The Art of Computer Programming, Vol. 2 , 1981 .

[15]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[16]  Telba Z Irony,et al.  Exact tests for equality of two proportions: Fisher × Bayes , 1985 .

[17]  M. Degroot.  Optimal Statistical Decisions , 1970 .

[18]  Christoph W. Ueberhuber,et al.  Computational Integration , 2018, An Introduction to Scientific, Symbolic, and Graphical Computation.

[19]  M. Aitkin.  Posterior Bayes Factors , 1991 .

[20]  Carlos Alberto de Bragança Pereira,et al.  ON THE CONCEPT OF P-VALUE , 1988 .

[21]  A. Gupta,et al.  A Bayesian Approach to , 1997 .

[22]  K. Popper,et al.  Conjectures and refutations;: The growth of scientific knowledge , 1972 .

[23]  D. Lindley.  A STATISTICAL PARADOX , 1957 .

[24]  J D Pinter,et al.  Global Optimization in Action—Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications , 2010 .

[25]  Calyampudi Radhakrishna Rao,et al.  Quality Control and Reliability. , 1989 .

[26]  Joel H. Saltz,et al.  Parallel Programming Using C++ , 1996 .

[27]  H. Jeffreys.  Logical Foundations of Probability , 1952, Nature.

[28]  Donald E. Knuth,et al.  The art of computer programming. Vol.2: Seminumerical algorithms , 1981 .

[29]  Carlos Alberto de Bragança Pereira,et al.  BAYESIAN HYPOTHESIS TEST: Using Surface Integrals to Distribute Prior Information Among the Hypotheses , 1995 .

[30]  Julio Michael Stern,et al.  Evidence and Credibility: Full Bayesian Significance Test for Precise Hypotheses , 1999, Entropy.