우도원리에 대한 분석과 그에 따른 교육적 시사점에 대한 연구
A Study on Analysis of Likelihood Principle and its Educational Implications
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This study analyzes the likelihood principle and elicits an educational implication. As a result of analysis, this study shows that Frequentist and Bayesian interpret the principle differently by assigning different role to that principle from each other. While frequentist regards the principle as 'the principle forming a basis for statistical inference using the likelihood ratio' through considering the likelihood as a direct tool for statistical inference, Bayesian looks upon the principle as 'the principle providing a basis for statistical inference using the posterior probability' by looking at the likelihood as a means for updating. Despite this distinction between two methods of statistical inference, two statistics schools get clues to compromise in a regard of using frequency prior probability. According to this result, this study suggests the statistics education that is a help to building of students' critical eye by their comparing inferences based on likelihood and posterior probability in the learning and teaching of updating process from frequency prior probability to posterior probability.
Abstract
This study analyzes the likelihood principle and elicits an educational implication. As a result of analysis, this study shows that Frequentist and Bayesian interpret the principle differently by assigning different role to that principle from each other. While frequentist regards the principle as 'the principle forming a basis for statistical inference using the likelihood ratio' through considering the likelihood as a direct tool for statistical inference, Bayesian looks upon the principle as 'the principle providing a basis for statistical inference using the posterior probability' by looking at the likelihood as a means for updating. Despite this distinction between two methods of statistical inference, two statistics schools get clues to compromise in a regard of using frequency prior probability. According to this result, this study suggests the statistics education that is a help to building of students' critical eye by their comparing inferences based on likelihood and posterior probability in the learning and teaching of updating process from frequency prior probability to posterior probability.
참고문헌 (50)
- 교육부, "수학과 교육과정(교육부 고시 제2015-74호)", ~ (2015)
- 김달호, "R과 WinBUGS를 이용한 베이지안 통계학(제2판)" (2013), 자유아카데미
- 김우철, "현대통계학" (2001), 영지문화사
- 김혜랑, "가능성 원리지도를 위한 중등 통계 교육과정의 개선 방향", 석사, 수학교육, pp.2004
- 서울대학교 교육연구소, "교육학 용어사전" (2000), 하우동설
- 송상헌, "수학교육학 연구 방법" (2013), 경문사
- 신수영, "초·중·고등학교 확률과 통계단원에 나타난 표본개념에 대한 분석", 석사, 수학교육, pp.2011
- 우정호, "수학교육학 연구방법론" (2007), 경문사
- 이경화, "확률 개념의 교수학적 변환에 관한 연구", 박사, 수학교육, pp.1996
- 이영하, "개인적인 면담 및 의사교환", ~ (2016)
- 이영하, "확률·통계 연구에 대한 수학교육학적 고찰 : <수학교육>에 게재된 논문을 중심으로", 수학교육, 42(2), pp.203~218 (2003), 한국수학교육학회
- 이영하, "분포 개념의 연계성 목표 관점에 따른 중학교 확률 단원 분석", 수학교육학연구, 20(2), pp.163~183 (2010), 대한수학교육학회
- 이은희, "국내외 통계교육 연구동향 비교 분석", 수학교육, 54(3), pp.241~259 (2015), 한국수학교육학회
- 이정연, "조건부확률 개념의 이해에 관한 연구", 석사, 수학교육, pp.2005
- 허지영, "분포 개념의 연계성에 따른 중학교 2학년 확률 단원 분석", 석사, 수학교육, pp.2010
- Albert, J., "Teaching Inference about Proportions Using Bayes and Discrete Models", Journal of Statis tics Education, 3(3) (1995)
- Berger, J., "The likelihood principle" (1988), IMS
- Berger, J., "Lectures notes in statistics" (1988), Springer-Verlag
- Birnbaum, A., "On the foundations of statistical inference", Journal of the American Statistical Association, 57, pp.269~326 (1962)
- Borovcnik, M. G., "Revising probabilities according to new information : A fundamental stochastic intuition", Proceedings of the Second International Conference on Teaching Statistics, pp.298~302 (1986)
- Chatterjee, S. K., "Statistical thought ; A perspective and history" (2003), Oxford University Press
- Cornfield, J., "Sequential trials, sequential analysis, and the likelihood principle", American Statistician, 29, pp.18~23 (1966)
- Dale, A. I., "A history of inverse probability: From Thomas Bayes to Karl Pearson" (1991), Springer-Verlag
- Edwards, A. W. F., "Commentary on arguments of Thomas Bayes", Scandinavian Journal of Statistics, 5, pp.116~118 (1978)
- Edwards, A. W. F., "Likelihood : Expanded edition" (1992), The Johns Hopkins University Press
- Falk, R., "Conditional probabilities : Insights and difficulties", Proceedings of the Second International Conference on Teaching Statistics, pp.992~997 (1986)
- Gandenberger, G., "A new proof of the likelihood principle", The British Journal for the Philosophy of Science, 66(3), pp.475~503 (2015)
- Gillispie, C., "Pierre-Simon Laplace 1749-1827 : A life in exact science" (1997), Princeton University Press
- Hacking, I., "Logic of statistical inference" (1965), Cambridge University Press
- Hacking, I., "The emergence of probability" (1999), Cambridge University Press
- Howie, D., "Interpreting probability: Controversies and developments in the early twentieth century" (2002), Cambridge University Press
- Konold, C., "Radical Constructivism in Mathematical Education", pp.139~156 (1991)
- Martin, R., "Discussion : Foundations of statistical inference, Revisited", Statistical Science, 29(2), pp.247~251 (2014)
- Mayo, D., "On the Birnbaum argument for the strong likelihood principle", Statistical Science, 29(2), pp.227~239 (2014)
- McGrayne, S. B., "불멸의 이론" (2013), 휴먼사이언스
- is the One True Measure of Confirmation, "Philosophy of Science", 1996, 21~26
- Pawitan, Y., "In all likelihood - Statistical modelling and inference using likelihood" (2001), Clarendon Press
- Rossman, A. J., "Conditional pro bability and education reform : Are they compatible?", Journal of Statistics Education, 3(2) (1995)
- Royall, R. M., "Statistical evidence: A likelihood paradigm" (1999), Chapman & Hall
- Salmon, W. C., "과학적 추론의 기초" (1994), 서광사
- Salsburg, D., "천재들의 주사위 - 20세기를 만든 통계학의 혁명들" (2003), 뿌리와이파리
- Savage, L., "Foundations of statistical inference: A discussion" (1962), Methuen
- Sober, E., "Reconstructing the past: Parsimony, evolution, and inference" (1988), MIT Press
- Steel, D., "A bayesian way to make stopping rules matter", Erkenntnis, 58, pp.213~227 (2003)
- Steel, D., "Bayesian confirmation theory and the likelihood principle", Synthese, 156(1), pp.53~77 (2007)
- Stigler, S. M., "The history of statistics: The measurement of uncertainty before 1900" (1986), Harvard University Press
- Stigler, S. M., "Statistics on the table: The history of statistical concepts and methods" (1999), Harvard University Press
- Stigler, S. M., "통계학의 역사" (2010), 한길사
- Tomlinson, S., "Understanding conditional probability", Teaching Statistics, 19(1), pp.2~7 (1997)
- Watson, J. M., "Conditional probability : Its place in the mathematics curriculum", Mathematics Teacher, 88(1), pp.12~17 (1995)