Stat 640: Advanced Statistical Theory
Department of Statistics and Biostatistics, CSU East Bay
Fall 2024:
Week 12:
- Topics: Fisher’s Information, Asymptotic Normality of the MLE, Asymptotic Confidence Intervals, CRLB, Method of Moments Estimation
- Homework: Homework 6 due date this week.
Week 11:
- Topics: MLE, Bootstrap, “irregular estimation”, Large Sample Theory of the MLE, \(AV(\hat{\theta})\)
- Midterm: Midterm 2 take-home will be posted in Canvas.
- Reference Books:
- Homework: Homework 6 due date has been extended until next week.
Week 10:
- Topics: Likelihood and Maximum Likelihood Estimation (MLE)
- Quiz: Quiz 2 will be given in class on Monday.
- Midterm: Midterm 2 will be take-home and will be made available next week on Monday.
Week 9:
- Topics: Derived Distributions, Survey Sampling, Method of Moments Estimation, Likelihood and Maximum Likelihood Estimation
- Handouts: Survey Sampling Handout has been posted.
- Assignment: Homework 6 has been posted.
- Python:
Week 8:
- Topics: Prediction, Law of Large Numbers, the Central Limit Theorem.
- Handouts: Handouts on the Law of Large Numbers and Central Limit Theorem have been posted.
- Upskill, 5 minute AI:
Week 7:
- Midterm: The Midterm will be given in class on Monday.
- Topics: Markov’s Inequality, Chebyshev’s Inequality.
- Assignment: Homework 5 has been posted.
- Upskill, 5 minute AI:
- Mistral.ai Frontier AI in your hands
- Mistral Console The easiest way to build Agents and RAG
Week 6:
- Quiz: Quiz on Monday. We will go over the solution to the Quiz on Wednesday.
- Midterm: The Midterm will be given in class on Monday, September 30.
- On Wednesday we will go over the topics of the Midterm.
Week 5:
- Quiz: Quiz 1 will be given in class on Monday, September 23. The quiz will cover material from the first five weeks of class. There will be a questions about choosing a Probability Model for a Random Variable. Review all of the Probability Models that we have discussed in class, know the random variables they model, know the parameters of the model, and know their expectations and variances. Transformation of random variables CDF Method. Review the Inverse CDF Method for Random Number Simulation.
- Midterm: The Midterm will be given in class on Monday, September 30.
- Topics: Order Statistics, Minimum and Maximum, Quantiles. The Exponential Distribution. The Gamma Distribution. Transformation of random variables, PDF Method. Box-Muller algorithm for normal random number generation.
- Assignment: Homework 3 is due this week. Homework 4 is due next week.
- Homework Guidelines: homework_guidelines.docx
- Upskill, 5 minute AI:
- Msty The easiest way to use local and online AI models
Week 4:
- Topics: Functions of Random Variables. Proposition C and Proposition D. Inverse CDF Method for generating random numbers. Joint Distributions and Conditional Distributions.
- Assignment: Homework 4 has been posted.
- Upskill, 5 minute AI: Cohere LLM University.
Week 3:
- Topics: Joint Distributions, Marginal Distributions, and Conditional Distributions.
- Assignment: Homework 3 has been posted.
- Canvas can accept a Website URL to your Google Colab Notebooks. Please submit a shared link to your Google Colab Notebook when submitting your homework.
Week 2:
- In class we will start with a few Probability Examples that use Independence. See the Handouts link.
- Topics: Probability Simulation, Random Variables, Probability Models, Simulation of Random Values.
- In class we will start with a discussion of Probability Models that can be described using an urn model.
- Homework submission: should be done through Canvas. Your papers should be submitted in the order assigned. Your name should appear on each page. I would suggest starting each problem at the top of a new page so it is clear to me which problem you are working on.
- Assignment: Homework 2 has been posted.
- Holiday: Monday, September 2nd is Labor Day. There will be no class.
- Unfortunately Canvas cannot display .ipynb files. Please upload a .docx file with a shared link to your Google Colab Notebook.
- Upskill, 5 minute AI: Run AI/LLMs online.
- Microsoft Edge with Copilot
- Brave with Leo AI
- Opera with Aria AI
- Chrome with Gemini
- Vivaldi the anti-AI browser
- duckduckgo.com/chat
- groq.ai
- cerebras.ai
Week 1:
- In class we will go over the syllabus.
- The lectures will be available through Zoom during the class times and the recording will be posted in Canvas.
- The book for the course will contain Python.
- Code for the book.
- Colab code for Chapter 1.
Week 0:
- Welcome to Statistics 640.
- The book for the course will contain Python.