Volume 19, Issue 2 (12-2020)                   JIRSS 2020, 19(2): 101-117 | Back to browse issues page

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Zolfaghari P, Chinipardaz R, Esmaily J. Testing a Point Null Hypothesis against One-Sided for Non Regular and Exponential Families: The Reconcilability Condition to P-values and Posterior Probability. JIRSS. 2020; 19 (2) :101-117
URL: http://jirss.irstat.ir/article-1-605-en.html
Department of Statistics, Faculty of Mathematics and Computer Science, Shahid Chamran University of Ahvaz, Ahvaz, Iran. , chinipardaz_r@scu.ac.ir
Abstract:   (365 Views)

In this paper, the reconcilability between the P-value and the posterior probability in testing a point null hypothesis against the one-sided hypothesis is considered. Two essential families, non regular and exponential family of distributions, are studied. It was shown in a non regular family of distributions; in some cases, it is possible to find a prior distribution function under which P-value and posterior probability are achieved. However, in the exponential family of distributions, this agreement is based on the complete monotonicity of a function of hazard rate.

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Type of Study: Original Paper | Subject: 62Fxx: Parametric inference
Received: 2019/07/27 | Accepted: 2021/03/25 | Published: 2020/12/11

1. Berger, J. O. (1985), Statistical Decision Theory and Bayesian Analysis, 2nd ed. Berlin, Springer Verlag. [DOI:10.1007/978-1-4757-4286-2]
2. Berger, J. O. and Delampady, M. (1987), Testing Precise Hypotheses (with discussion). Statistical Science, 2, 317-352. [DOI:10.1214/ss/1177013238]
3. Berger, J. O. and Sellke, T. (1987), Testing a Point Null hypotheses: The Irreconcilability of P-values and Evidence (with discussion). Journal of the American Statistical Association, 82, 112-139. [DOI:10.2307/2289131]
4. Casella, G. and Berger, R. L. (1987), Reconciling Bayesian and Frequentist Evidence in the One-Sided Testing Problem. Journal of the American Statistical Association, 82, 106-111. [DOI:10.1080/01621459.1987.10478396]
5. Chinipardaz, R. (2003), The Discrepancy of P-values and Posterior Probability in Poisson Distribution. Pakistan Journal of Statistics, 19, 301-313.
6. Chinipardaz, R. and Noorbaloochi, S. (2003), The reconcilability of P-values and posterior probability in nonregular distributions. Far east Journal of Theoretical Statistics, 10, 112-122.
7. DeGroot, M. H. (1973), Dowing what comes naturally: Interpretaing a tail area as a posterior probability or likelihood ratio. Journal of the American Statistical Association, 68, 966-969. [DOI:10.1080/01621459.1973.10481456]
8. Delampady, M. (1989), Lower bound on Bayes Factors for Interval Null Hypotheses. Journal of the American Statistical Association, 84(405), 120-124. [DOI:10.1080/01621459.1989.10478746]
9. Dickey, J. M. (1977), Is the tail area useful as an approximate Bayes factor ?. Journal of the American Statistical Association, 72, 138-142. [DOI:10.1080/01621459.1977.10479922]
10. Edwards, W., Lindman, H. and Savage, L. J. (1963), Bayesian Statistical Inference for Psychological Research. Psychological Review, 70(3), 193-242. [DOI:10.1037/h0044139]
11. Efron, B. and Gous, A. (2001), Scale of evidence for model selection: Fisher versus Jeffrey Model Selection, In: Lecture Notes - Monograph Series. Institute of Mathematical Statistics, 38, 208-256. [DOI:10.1214/lnms/1215540972]
12. Feller, W. (1971), An Introduction to Probability Theory and its Applications. Vol. 2, NewYork, John Wiley.
13. Lindley, D. V., (1957), A Statistical Paradox. Biometrika, 64, 207-213. [DOI:10.1093/biomet/64.2.207]
14. Mayo, D. (2006), Philosophy of statistics. In: S. Sarkar, S. and Pfeifer, J. Eds. The Philosophy of Science: an encyclopedia. London: Routledge, 802-815.
15. Nickerson, R. S. (2000), Null hypothesis significance testing: A review of on old and continuing controversy. Psychological Methods, 5(2), 241-301. [DOI:10.1037/1082-989X.5.2.241]
16. Sellk, T., Bayarri, M. J. and Berger, J. O. (2001), Calibration of P-values for Testing Precise Null Hypotheses. The American Statistician, 55, 62-71. [DOI:10.1198/000313001300339950]
17. Verdinell, I. and Wessermann, L. (1998), Bayesian goodness of fit testing using infinite dimensional exponential families. The Annals of Statistics, 26(4), 1215-1241. [DOI:10.1214/aos/1024691240]

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