Fundamentals of Statistical Inference
| Numbering Code | P-PUB01 8H136 LJ90 | Year/Term | 2022 ・ First semester | |
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| Number of Credits | 2 | Course Type | lecture and seminar | |
| Target Year | Professional degree students | Target Student | ||
| Language | Japanese | Day/Period | Thu.4 | |
| Instructor name |
SATO TOSIYA (Graduate School of Medicine Professor) HENMI MASAYUKI (Part-time Lecturer) OMORI TAKASHI (Graduate School of Medicine Program-Specific Professor) Omiya Masatomo (Graduate School of Medicine Program-Specific Assistant Professor) |
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| Outline and Purpose of the Course |
In this course, students will learn the fundamentals of statistics-related subjects. The first will deal with the fundamentals of probability theory, which form the foundation for methods of statistical inference. The second half will deal with the basic concepts of statistical inference such as statistical estimation, hypothesis testing, and confidence intervals. Probability theory in the first half is not based on mathematically rigorous measurement theories, but rather uses calculus and linear algebra (undergraduate-level mathematics) with the aim of teaching students the fundamentals of probability necessary to understand methods of statistical inference. The latter half of statistical inference emphasizes the fundamental ideas and theoretical aspects of the basic concepts. The aim of this course is preparation and consolidation while focusing on the fundamentals that we cannot stop to think about in the course of other statistics-related subjects. Since students in this course are expected to come from various backgrounds, lessons will proceed with as much consideration for their circumstances as possible. [Lecture format, using PowerPoint slides and whiteboards] |
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| Course Goals |
・Understand the meaning of and ways of thinking that underlie basic concepts related to probability and statistics, and be able to explain these in your own words. ・Be able to carry out calculations relating to statistics and probability distribution etc., while framing your own thoughts when necessary. ・While studying other statistics-related subjects, be capable of studying various statistic methods on your own, and understand their mechanisms without viewing them as a black box. |
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| Schedule and Contents |
Session 1, April 8: Lecture Overview and Probability and Stochastic Variable Concepts (Itsumi) Session 2, April 15: Fundamentals of Discrete Random Variables and their Distribution (Itsumi) Session 3, April 22: Fundamentals of Continuous Random Variables and their Distribution (Itsumi) Session 4, May 6: Handling Multiple Random Variables I (Henmi) Session 5, May 13: Handling Multiple Random Variables II (Henmi) Session 6, May 20: Probability Distributions for Normal Samples (Henmi) Session 7, May 27: Fundamentals of Statistical Estimates (Ohmae) Session 8, June 3: Fundamentals of Statistical Hypothesis Testing I (Imai) Session 9, June 10: Fundamentals of Statistical Hypothesis Testing II (Imai) Session 10, June 17: Fundamentals of Linear Regression Analysis (Henmi) Session 11, June 24: Fundamentals of Linear Regression Analysis II (Henmi) Session 12, July 1: Fundamental Asymptotic Methods I (Limit Theorem, Maximum Likelihood, and its Properties) (Henmi) Session 13, July 8: Fundamental Asymptotic Methods II (Tests based on Maximum Likelihood) (Henmi) Session 14, July 15: Fundamental Asymptotic Methods III (Delta method, methods of estimation other than the maximum likelihood method) (Henmi) |
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| Evaluation Methods and Policy | Reports | |||
| Course Requirements |
・Students must have basic knowledge of calculus and linear algebra. ・We do not accept human health science majors. |
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| Study outside of Class (preparation and review) |
・We expect students taking this course to learn various things, but we would like for them to emphasize on the parts that they do not fully understand while taking advantage of this class. ・Attendance at lectures alone is insufficient to understand and master the content of mathematical lessons. It is necessary to work through these one your own, checking calculations and logic after each lecture. The content covered in this lecture is very important to understand other statistics-related courses involving mathematical elements, so students are advised to work diligently on reviewing all that they learn. ・In addition to this class, other seminars are arranged for as part of the Clinical Statistician Training course. Those who are unsure of the basics, or are experiencing difficulty with the exercises themselves should also make use of these seminars. |
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| Textbooks | Textbooks/References | Lecture materials will be distributed. | ||
| References, etc. | Other materials will be introduced during lectures | |||
