Following Lee (1997, pp. 123-124), Lindley (1965, 58-62), and Zellner (1971, pp. 298-302), I have been using Lindley's method of 95% credible intervals under a diffuse prior to determine whether a parameter is 'significant'.  However,  Bernardo & Smith (1994, p. 395) remind us that the width of the credible interval should be based on decision-theory.  From their very brief analysis, a 50% interval has considerable justification and the 95% interval much less so.  Are there more recent references on this problem?  Does anyone have any further thoughts?  I would hate to see the 95% interval, obviously culled from frequentist analyses, continued in use solely from cognitive inertia.
 
Joe
 

Bernardo, J. M., & Smith, A. F. M. (1994). Bayesian theory. Chichester: Wiley.

Lee, P. M. (1997). Bayesian statistics: An introduction (2nd ed.). London: Arnold.

Lindley, D. V. (1965). Introduction to probability and statistics from a Bayesian viewpoint: Inference (Vol. 2). Cambridge, UK: Cambridge University Press.

Zellner, A. (1971). An introduction to Bayesian inference in econometrics. Cambridge, UK: Cambridge University Press.

 

Joseph F. Lucke, PhD

Statistical Scientist

Family Nursing Care (MC 7951)

School of Nursing

University of Texas Health Science Center at San Antonio

7703 Floyd Curl Drive

San Antonio, TX 78229-3900

Voice: 210 567 0474

Fax:    210 567-5822

www.uthscsa.edu

 
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