Probability and Statistics

Course title

A0013000

	ISHIWATA Gen
	TSUNODA Kazumi

Course description

Statistics is the scientific method for the demonstration study based on data. The field that statistics treat is used for not only natural science but also
cultural science, social science, life science and environmental science, etc., and all of these studies.
The purpose of Statistics is to analyze and correlate acquired data into a useable experiment for observation, resulting in the testing of a hypothesis.
This skill is always necessary in almost all study fields, and a scientific conclusion is reached by the judgment based on statistics. This is way, this is
said to be the "Grammar of science". Furthermore, statistics are the application of measurement techniques in order to understand and give meaning
to the data being analysed. Statistical principles are criterion, too.
Therefore, it is possible to treat the enormous quantity of data in modern days by the enhancement of the information network. In the world of
science, the concept "Data Science" is introduced as a paradigm of the fourth science following experimental science, theoretical science, and
computing science. This is becoming an indispensable science, and has increased the importance of statistics.
Thus, it is important to understand a smooth connection from an inductive idea to the deductive thought to use statistics correctly, (In other words,
mathematics is deductive thinking only, whereas science is inductive thinking only; however, statistics is a combination of both ways of thinking);
and data is always needed in order to understand it.
In this lecture, I explain various statistical analysis techniques based on an essential feature of such statistics.

Purpose of class

Statistics is used for all scientific judgements, and it is common knowledge that is basic to any field.
This study course is to acquire a fundamental method of the statistics that should be studied in university undergraduate education, and become
able to use the appropriate statistics method for a given scenario.
Moreover, a second, but just as important purpose, is to become able to understand and interpret the meaning of publicly-available documents and
statistical data from both the government and private companies.

Goals and objectives

To use "Descriptive scale" for summarizing of data and to visualize data.
To calculate probability of the phenomenon, and to understand the meaning of probability variable and the probability distribution.
To understand the concept of the central limit theorem, and to understand the relation to the random sampling.
To apply various statistical analytical techniques according to the purpose, and to make conclusions.
To acquire data of the problem of reality, and to do the problem solution based on statistical thinking.

Relationship between 'Goals and Objectives' and 'Course Outcomes'

	Midterm examination	Report	Final examination	Total.
1.		2%	3%	5%
2.	18%	6%	6%	30%
3.	2%	2%	1%	5%
4.		10%	20%	30%
5.		20%	10%	30%
Total.	20%	40%	40%	-

Evaluation method and criteria

Final Exam:50%, Midterm:20%, Report:30% = Total:100%
General Evaluation: Over60% to pass.

Language

Japanese

Class schedule

	Class schedule	HW assignments (Including preparation and review of the class.)	Amount of Time Required
1.	Descriptive Statistics[Data Analysis] ・Look at the data 　　（Histogram, Box-and-whisker plot, Scatter diagram, Frequency distribution table, Mean(average), Variance, Median）	・Review：Descriptive scale and chart or graph making	190minutes
2.	Probability 1 ・Phenomenon and probability 　　（Phenomenon and probability, Axioms of probability, Formula of probability, Conditional probability, Bayes' theorem）	・Practice: with ”Probability 1” paper.	190minutes
3.	Probability 2 ・Random variable and probability distribution 1 　　（Random variable/ Discrete probability distribution(Discrete uniform distribution, Binomial distribution, Poisson distribution, Hypergeometric distribution, Geometric distribution)）	・Practice: with ”Probability 2” paper.	190minutes
4.	Probability 3 ・Random variable and probability distribution 2 　　（Random variable/ Continuous probability distribution(Uniform distribution, Normal distribution, Student's t-distribution, Gamma distribution, Exponential distribution, Chi-squared distribution, F-distribution)）	・Practice: with ”Probability 3” paper.	190minutes
5.	Probability 4 ・Central limit theorem 　　（Cumulative distribution function, Moment generating function, Chebyshev's inequality, Law of large number, Central limit theorem）	・Review : Central limit theorem	190minutes
6.	Midterm examination ・Mini-test and Explanation 　　（Test on “probability”, Explanation） Inferential statistics[Mathematical statistics]1 ・Statistics Over View　　（Statistical thinking, Random sample, Population and sampling distribution, Unbiased estimation and Consistency of estimators）	・Practice problem on the probability	200minutes
6.		・Practice: with ”Inferential statistics 1” paper.
7.	Inferential statistics[Mathematical statistics]2 ・Point estimation and Interval estimation 　　（Point estimation, Standardizing, Statistic, Interval estimation of mean）	・Practice: with ”Inferential statistics 2” paper.	200minutes
8.	Inferential statistics[Mathematical statistics]3 ・Statistical hypothesis testing 　　（The testing process, Type I and type II errors, Hypothesis Test for a Mean (When population variance is known), In one sample tests for a dichotomous outcome, Student's t-test, Hypothesis testing of a single population variance, F-test）	・Practice: with ”Inferential statistics 3” paper.	200minutes
9.	Inferential statistics[Mathematical statistics]4 ・Correlation analysis and Regression analysis 　　（Multivariate probability distributions, Covariance, Pearson's product-moment coefficient, Fisher transformation, Linear regression model, Method of least squares, Regression residuals, Coefficient of determination, Multiple regression）	・Report studies start.	100minutes
9.		・Practice: with ”Inferential statistics 4” paper.	100minutes
10.	Inferential statistics[Mathematical statistics]5 ・Analysis of variance(ANOVA) and Test for fit of a distribution 　　（Pearson's chi-squared test, Level of factor, One-way analysis of variance, Two-way analysis of variance, Main effect model）	・Practice: with ”Inferential statistics 5” paper.	100minutes
10.		・Report studies.	100minutes
11.	Inferential statistics[Mathematical statistics]6 ・Non-Parametric Model　　（Ordinal ranking, Sign test, Ranklet, Rank sum test, Rank correlation, Runs test）	・Practice: with ”Inferential statistics 6” paper.	100minutes
11.		・Report studies.	100minutes
12.	Inferential statistics[Mathematical statistics]7 ・Quality control(QC) 　　（Control limit, Control sampling inspection, Operating characteristic curve, Process capability index / Integrated study）	・Practice: with ”Inferential statistics 7” paper.	100minutes
12.		・Report studies.	100minutes
13.	Inferential statistics[Mathematical statistics]8 ・Akaike information criterion(AIC) 　　（Method of maximum likelihood, Maximum log likelihood, Kullback‒Leibler divergence, Model selection, Akaike information criterion(AIC)）	・Report submission deadline. (report will be collected at this time)	100minutes
13.		・Practice: with ”Inferential statistics 8” paper.	100minutes
14.	Final examination ・Term examination and general comment 　　（Test on “statistics”, Explanation, Evaluation of report, General comment）	・Review: All practice papers.	200minutes
Total.	-	-	2750minutes

Feedback on exams, assignments, etc.

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Textbooks and reference materials

1)Textbook：「日本統計学会公式認定[統計検定2級対応] 改訂版統計学基礎」　日本統計学会編（東京図書） in Japanese
2)Reference：「基礎統計学1　統計学入門」　東京大学教養学部統計学教室編 (東京大学出版会) in Japanese
3)Practice Book： Elementary Statistics (Wiley Series in Probability and Statistics - Applied Probability and Statistics Section) 4th Edition

If you are an international student, and if you need textbooks or reference books, then please consult me.

Prerequisites

Ideally, you should have already finished the following subjects.
"Linear Algebra 1", "Linear Algebra 2", "Differential and Integration 1" and "Differential and Integration 2"

Office hours and How to contact professors for questions