Probabilistic and Statistical Analysis and Exercise

Numbering Code U-ENG23 23003 LJ55 Year/Term 2021 ・ First semester
Number of Credits 2 Course Type Seminar
Target Year Target Student
Language Japanese Day/Period Tue.3・4
Instructor name HORI TOMOHARU (Disaster Prevention Research Institute Professor)
Outline and Purpose of the Course Understanding the theory and method of probability statistical analysis as a basic method to cope with the uncertainty of natural and social phenomena subject to geotechnology. In particular, the goal is to understand the concept of probability and its basic theorem, master basic probability distribution and its usage, master thinking on statistical estimation tests, and understanding the basic methods of multivariate analysis. The lecture is a parallel lecture divided into four classes.
Course Goals Getting familiar with the concept of probability and the basic theorem, and understanding various distributions that are widely used in the field of geotechnology and its properties and usage for design, and so forth. Additionally, being able to understand the basic nature of populations and specimens and the principles of estimation and verification and using them for concrete inferential statistics.
Schedule and Contents The 1st Class: Significance of probability statistical method
A lecture will be given on the significance, in terms of engineering, of probability statistics, and the necessity in general engineering will be outlined.

The 2nd - 5th Classes: Probabilistic grasp of uncertain phenomena
The concept of probability and its basic theorem will be explained. In particular, conditional probability, random variables, the probability distribution function, the probability density function, the moment generating function, and the characteristic function will be explained. Multidimensional probability distribution and the transformation of random variables will also be discussed.

The 6th - 9th Classes: Probability distribution model
The characteristics and properties of various probability distributions effective for expressing real phenomena such as binomial distribution, Poisson distribution, normal distribution, and so forth will be described.

The 10th - 12th Classes: Sample distribution and statistical estimation/test
Sample distribution, such as X^2 distribution, t distribution, F distribution, and how to calculate them will be explained. In addition, regarding statistical estimations to derive probabilistic properties of a population from sample values, a lecture will be given on the concept and method of point and interval estimation, and the statistical test method to verify the significance of engineering phenomena.

The 13th - 14th Classes: Multivariate statistical analysis/regression analysis
Based on the theory of probability statistics, multivariate analysis and the method of analysis of variance that are mainly used to analyze survey data will be described. In particular, the probabilistic model and the confidence limits by taking the first order regression analysis as an example will be outlined.

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The 15th Class: Feedback
Evaluation Methods and Policy Grades will be evaluated by including the degree of active participation in lectures and exercises, the results of quizzes and intermediate tests, and so forth in the scores of regular tests. The details will be communicated by the professors at the beginning of the class. A passing score is 60 or more out of 100 points.
Course Requirements It is desirable that students have taken calculus and linear algebra.
Study outside of Class (preparation and review) It is necessary to review based on lecture materials and to complete the report assignments given during the lecture.
Textbooks Textbooks/References An Introduction to Probability and Statistics for Engineering, Kitamura,S and Hori,T(eds.): , (Asakura Publishing Co., Ltd., ), ISBN:9784254111132
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