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Statistics

Mathematical Statistics, Part I

Build on probability to study sampling, point estimation, bias, consistency, and efficiency.

Instructor Dr. Waleed A. Yousef Adjunct Professor, University of Victoria, Canada
A bell-shaped population of spheres with a smaller sample in a glass dish

01

Course overview

Build on probability to study sampling, point estimation, bias, consistency, and efficiency.

02

What you will learn

In this new course, I will build upon my previous course, "Probability," which was based on John Rice's textbook. In that course, I covered roughly the first half or one-third of the book.

In this new course, "Mathematical Statistics: Part I," I will continue by teaching Chapter 6 and Chapter 8, which are the fundamental building blocks of statistics. These chapter provide basics of statistics, sampling, and point estimation. You’ll learn how to derive estimators and understand their properties, such as bias, consistency, and efficiency. This is the first course in a series of three aimed at covering the remaining chapters of this textbook.

This course, and the entire series, are fundamental for scientists who want to gain a rigorous understanding, develop intuitive insights, and learn practical applications of Mathematical Statistics. It is essential for scientific fields and especially critical for those pursuing machine learning.

03

Lecture syllabus

Video titles and durations as published on Arabsera. The advertised lecture total may differ from the number of video entries, which can include introductions, tutorials, and split sessions.

Video titles and durations 12
  1. 00 Introduction and Motivation: why Statistics?
  2. 01 Sec. 6.1 Gamma Distribution and Introduction
  3. 02 Sec. 6.2--6.3 Important Distributions and Sampling
  4. 03 Sec. 6.3 cont.
  5. 04 Sec. 8.1--8.4 Method of Moments
  6. 05 Sec. 8.5 MLE
  7. 06 Sec. 8.5 MLE cont.
  8. 07 Sec. 8.6 Bayesian Estimation
  9. 08 Sec. 8.6 Bayesian Estimation cont.
  10. 09 Sec. 8.7 Assessment, Efficiency, and Bounds (frequentist)
  11. 10 Sec. 8.7 Assessment, Efficiency, and Bounds (Bayesian)
  12. 11 Sec. 8.8 Sufficient Statistics

04

Teaching support (check your plan)

  • Discussion groups
  • TA-human texting for Q&A
  • TA-GPT (coming soon)

05

Textbook

Rice, J.A., “Mathematical statistics and data analysis”. 3rd ed.

06

Certificate

Awarded upon completion of all course activities.