全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

A Note on the Connection between Likelihood Inference, Bayes Factors, and P-Values

DOI: 10.4236/oalib.1103292, PP. 1-11

Subject Areas: Applied Statistical Mathematics

Keywords: Hypothesis Testing, Likelihood Principle, Statistical Evidence

Full-Text   Cite this paper   Add to My Lib

Abstract

The p-value is widely used for quantifying evidence in a statistical hypothesis testing problem. A major criticism, however, is that the p-value does not satisfy the likelihood principle. In this paper, we show that a p-value assessment of evidence can indeed be defined within the likelihood inference framework. Included within this framework is a link between a p-value and the likelihood ratio statistic. Thus, a link between a p-value and the Bayes factor can also be highlighted. The connection between p-values and likelihood based measures of evidence broaden the use of the p-value and deepen our understanding of statistical hypothesis testing.

Cite this paper

Neath, A. A. (2017). A Note on the Connection between Likelihood Inference, Bayes Factors, and P-Values. Open Access Library Journal, 4, e3292. doi: http://dx.doi.org/10.4236/oalib.1103292.

References

[1]  Wasserstein, R. and Lazar, N. (2016) The ASA’s Statement on p-Values: Context, Process, and Purpose. The American Statistician, 70, 129-133.
https://doi.org/10.1080/00031305.2016.1154108
[2]  Efron, B. (2013) Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction. Cambridge University Press, Cambridge.
[3]  Gelman, A. and Robert, C. (2013) Revised Evidence for Statistical Standards. Proceedings of the National Academy of Sciences, 111, 19.
[4]  Pawitan, Y. (2013) In All Likelihood: Statistical Modelling and Inference Using Likelihood. Oxford University Press, Oxford.
[5]  Berger, J. and Wolpert, R. (1988) The Likelihood Principle: A Review, Generalizations, and Statistical Implications. Institute of Mathematical Statistics, Hayward, CA.
[6]  MacKenzie, D. (2002) Euro Coin Accused of Unfair Flipping. New Scientist.
http://www.newscientist.com/article/dn1748
[7]  Agresti, A. (2013) Categorical Data Analysis. Wiley, Hoboken, NJ.
[8]  Sellke, T., Bayarri, M. and Berger, J. (2001) Calibration of p-Values for Testing Precise Null Hypotheses. The American Statistician, 55, 62-71.
https://doi.org/10.1198/000313001300339950
[9]  Hubbard, R. and Bayarri, M. (2003) p-Values Are Not Error Probabilities. Institute of Statistics and Decision Sciences, Working Paper No. 03-26.
[10]  Kass, R. and Raftery, A. (1995) Bayes Factors. Journal of the American Statistical Association, 90, 773-795.
https://doi.org/10.1080/01621459.1995.10476572
[11]  Goodman, S. (2001) Of p-Values and Bayes: A Modest Proposal. Epidemiology, 12, 295-297.
https://doi.org/10.1097/00001648-200105000-00006

Full-Text


comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133

WeChat 1538708413