大学院
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最終更新日：2026年4月20日
授業計画や教室は変更となる可能性があるため、必ずUTASで最新の情報を確認して下さい。
UTASにアクセスできない方は、担当教員または部局教務へお問い合わせ下さい。
最終更新日：2026年4月20日
授業計画や教室は変更となる可能性があるため、必ずUTASで最新の情報を確認して下さい。
UTASにアクセスできない方は、担当教員または部局教務へお問い合わせ下さい。
確率的シミュレーション
The objective of this course is to explore various aspects of Monte Carlo methods, a fundamental computational technique for simulating stochastic events and quantifying uncertainty. Beginning with an overview of sampling from probability distributions (i.e., random number generation), which is essential for "using" Monte Carlo methods, and then proceeding to methods of "improving" Monte Carlo methods for better computational efficiency (i.e., variance reduction techniques), the aim is to ensure a proper understanding of Monte Carlo methods and their skillful applications in practical use.
時間割／共通科目コード
コース名
教員
学期
時限
3736-143
GEN-SI5103L3
確率的シミュレーション
合田 隆
火曜2限
マイリストに追加
マイリストから削除
講義使用言語
日本語、英語
単位
1
実務経験のある教員による授業科目
NO
他学部履修
可
開講所属
工学系研究科
授業計画
1. Basics of stochastic simulation
-- Overview of stochastic simulation
-- Basic statistical measures
-- Estimation by Monte Carlo methods
2. Random number generation
-- Pseudo-random number generation
-- Inversion method
-- Transformation
-- Acceptance-rejection
-- Markov chain Monte Carlo sampling
3. Variance reduction: Part I
-- Antithetic sampling
-- Control variate
-- Common random numbers
-- Conditional Monte Carlo
-- Importance sampling
4. Multilevel Monte Carlo methods
-- Bias-variance decomposition
-- From control variate to 2-level Monte Carlo
-- Multilevel Monte Carlo
-- Application to nested expectations
5. Variance reduction: Part II
-- Stratified sampling
-- Latin hypercube designs
-- Quasi-Monte Carlo
6. Global sensitivity analysis
-- Local sensitivity analysis
-- Analysis of variance and global sensitivity analysis
-- Monte Carlo estimation of sensitivity measures
授業の方法
Each class consists of a lecture and a short exercise. Handouts will be uploaded on UTOL before each lecture. The short exercise is given on the last slide of each handout. Answers to the short exercises should be submitted through UTOL within the same day as the lecture (in PDF format).
成績評価方法
Weekly short quizzes (35%) and a final report (65%)
履修上の注意
Although most lectures cover theoretical aspects, the final assignment will require some programming skills. Any programming language can be used for the final assignment.
その他
＜前提となる知識・項目＞
Probability theory and statistics (undergraduate level in engineering), and programming
＜備考＞
* This course is primarily delivered in English.
** While the lectures mainly focus on theoretical aspects of stochastic simulation (Monte Carlo methods), computer programming is mandatory for the final report. Any programming language is acceptable.
*** The course materials corresponding to each lecture will be uploaded to UTOL in advance, so please study them beforehand. Additionally, after each lecture, it is recommended to review the course materials and your notes.
