Kun Meng (Mike, 孟琨)

"When you teach, you do something useful. When you do research, most days you don’t."

--- June Huh

You are welcome to download the latest version of the lecture notes here.

(This page is partly intended for students enrolled in STA-4321 (@FSU) and APMA 1660/1690/1655 (@Brown) to download lecture notes.)

STA-4321: Introduction to Mathematical Statistics

Department of Statistics, Florida State University
Semesters: Fall 2025.
Role: Instructor.
Lecture notes 👉

Lecture_Notes_of_STA-4321.pdf

APMA 1660: Statistical Inference II

Division of Applied Mathematics, Brown University.
Semesters: Spring 2024 (134 students), Spring 2025 (130 students).
Role: Instructor.
Lecture notes 👉

This course is designed for undergraduate students and serves as a sequel to APMA 1650 (Statistical Inference I) or APMA 1655 (Honors Statistical Inference I).

The course begins with the theory of maximum likelihood estimation in parametric statistics, using linear and logistic models as examples. It covers advanced theoretical concepts and computational algorithms, including the asymptotic normality of maximum likelihood estimators, the EM algorithm, and Newton's method.
Additionally, there is a brief introduction to the theory of reproducing kernel Hilbert spaces, with smoothing splines used as an example.
At the end of the course, students are exposed to an introduction to Bayesian statistics. The computational aspects of Bayesian statistics will be covered in a sequel to the course---APMA 1690.

APMA 1660 focuses primarily on the mathematical theory of statistics, particularly in light of the numerous applied statistics courses available from the Biostatistics and Data Science Institute at Brown (such as PHP 2510, 2514, 2515, 2550 in the Fall, and PHP 2511, 2516, 2517, 2650, DATA 2020 in the Spring).

Lecture_notes_of_APMA_1660.pdf

APMA 1690: Computational Probability and Statistics

Division of Applied Mathematics, Brown University.
Semesters: Fall 2022 (132 students), Fall 2023 (124 students), Fall 2025 (162 students).
Role: Instructor.
Lecture notes 👉
One homework assignment 👉

This course is designed for senior undergraduate students and graduate students in Data Science/Engineering/Computer Science/Physics. The primary focus of the course is on Monte Carlo methods.

The course begins with a review of probability theory, focusing on the definition of "true randomness." It then introduces pseudo-random number generators (PRNGs), with the multiplicative congruential generator (MCG) used as an example.
IID Monte Carlo methods are described. Their mathematical foundations---the law of large numbers (LLN) and the law of the iterated logarithm (LIL)---are discussed.
As a preparation for the Markov chain Monte Carlo (MCMC), the definition of Markov chains and Markov chain ergodic theorem are introduced.
Two MCMC algorithms are presented---the Metropolis-Hastings algorithm and Gibbs sampling. As an application, the Gibbs sampling is applied to the 2-dimensional Ising model.
Towards the end of the course, there is an introduction to manifold learning, with a particular focus on principal component analysis (PCA).

Lecture_Notes_of_APMA_1690_by_Kun_Meng.pdf

APMA1690_HW9.pdf

APMA 1655: Honors Statistical Inference I

Division of Applied Mathematics, Brown University.
Semesters: Spring 2023 (50 students).
Role: Instructor.
Lecture notes 👉

Students may opt to enroll in APMA 1655 for more in depth coverage of APMA 1650 (Statistical Inference I).

Lecture_Notes_of_APMA_1655.pdf

APMA 1971: Independent Study - WRIT

Division of Applied Mathematics, Brown University.
Semesters: Spring 2023 (2 students).
Role: Instructor.

APMA 1970: Independent Study

Division of Applied Mathematics, Brown University.
Semesters: Spring 2024 (1 student).
Role: Instructor.

PHP 2550: Practical Data Analysis

Department of Biostatistics, Brown University.
Semesters: Fall 2019.
Role: Teaching Assistant.

DATA 2020: Statistical Learning

Data Science Institute, Brown University.
Semesters: Spring 2020.
Role: Teaching Assistant.

Graduate-level Partial Differential Equations

School of Mathematical Sciences, Beijing Normal University.
Textbook: L. C. Evans. Partial Differential Equations. (Chapters 5 and 6.)
Role: I delivered several lectures on behalf of the course instructor.

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