Biostatistics 202C Bayes Theory

Fall 2021 - Robert Weiss

Course pages are updated for Fall 2021.

News and announcements:

• Finals week: Monday Dec 6, 11:30 -- 2:30, Room 61-262 CHS (same as regular classroom).
• Comments on presentations.
• HW #5 update to problem 1: you may, if you like, take $q=1$ and $z_{ij} = 1$.
• Nov 8: Student presentation schedule set. Posted here and to CCLE.
• Reminder: No class Nov 24.
• Reminder: Student presentations on Nov 29, Dec 1, Dec 6(finals week), target 15 minutes. 5 presentations each day.
• Fixed link for lecture notes 14b. Let me know if still a problem. (But hit reload first.)
• Internet has been flaky in the past and consequently it was hard to record lectures. My sincere apologies. Notes for all lectures are available below.
• What was covered on each day is listed down below on the Videos Available portion of this web page. Even if the corresponding video isn't available.
• All available Wednesdays' notes are posted on CCLE.
• 2021 Syllabus.
• Homeworks have been updated for 2021. They are all dated September 19, 2021 except Homework 4 is dated September 21, 2021. If your version of the homework pdfs are dated earlier than that, please download the new versions.
• Pick your paper, clear it with me, prepare 20 minute talk, send me slides, we will discuss slides to improve your talk. Ideally in a zoom meeting, or can do it via email. Repeat: send me revised slides, lets do two or more iterations.
• List of possible papers to present on. You may pick other papers. All papers (even in this list) need to be cleared with me. Everyone must pick a different paper.
• To turn in homeworks, please email one pdf per homework to Weiss, thanks.
• Presentation and report: A 20 minute talk and a report (3 page double spaced + figures & tables). No exams.
• Homeworks, Videos, and Lecture Notes will be password protected.
• Random Effects Summary sheets. For when lecture ends after notes 17a, as a quick summary.

Table of Contents

• Class Schedule
• General Information about Biostat 202C Bayes Theory
• Lecture Notes
• Wednesday Notes
• Videos Available on our CCLE course page
• Homework Assignments
• Homework Due Dates
• Old notes on Bayesian Theory.

2021 Class Schedule, Email Address, and Office Hours:

General Information about Biostat 202C Bayes Theory

1. This course is aimed at second year Biostatistics masters students and Biostatistics doctoral students. Graduate (usually doctoral) students with a strong quantitative background from other departments are encouraged to enroll. A necessary prerequisite is a good background in probability, calculus, mathematical statistics, and regression as for example from Biostat 200A, 200B, probability as in Biostat 202A, and some mathematical statistics as in Biostat 202B.
2. In particular, exposure to likelihood theory and to completing the square in the normal likelihood will be extremely useful and is likely necessary.
3. Mathematical background requires comfort with integration, differentiation, linear algebra and ugly algebraic manipulations.
4. Grading is based on homework and projects.
5. Course topics will include an overview of Bayesian theory, the mathematics underlying Bayesian methods, computation, the connection between conclusions and assumptions and data.
6. The lectures are based on notes which will be made available on the web. The notes will be the primary reading material.

Lecture Notes

• Syllabus.

• Homeworks, Handouts and Lecture Notes will be password protected.
• Handouts and Lecture
• Lecture Notes 1. Intro, overview.
• Lecture Notes 2. Normal approximations.
• Lecture Notes 3. Normal prior, normal likelihood.
• Lecture Notes 4. Binomial
• Lecture Notes 4a. Binomial and Uniform
• Lecture notes 4b. A Fish Story -- how a Poisson experiment and an exponential experiment produce the same likelihood for the unknown parameter.
• Lecture Notes 5. Normal, mu and sigma^2 unknown. Gamma data.
• Lecture Notes 6. Multivariate normal data. Variance known.
• Lecture Notes 7. Priors.
• Lecture Notes 8. More Priors.
• Lecture Notes 9. Regression.
• Lecture Notes 10. Model Selection I.
• Lecture Notes 11a. Model Selection IIa.
• Lecture Notes 11b. Model Selection IIb.
• Lecture Notes 12. Model Selection III.
• Lecture Notes 13. Computing I.
• Lecture Notes 14a. Computing II. Monte Carlo and Bayes factors. 1 of 2
• Lecture Notes 14b. Computing II. Monte Carlo and Bayes factors. 2 of 2
• Lecture Notes 15. Computing III. MCMC
• Lecture Notes 16. Computing IV. Importance Sampling.
• Lecture Notes 16a. Computing IV. Importance Sampling.
• Lecture Notes 16b. Computing IV. Diagnostics, Sensitivity Analysis.
• Lecture Notes 16c. Computing IV. Diagnostics, Sensitivity Analysis.
• Lecture Notes 17a. Hierarchical Models I.
• Random Effects Summary sheets. For when lecture ends after notes 17a, as a quick summary.
• Lecture Notes 17b. Hierarchical Models II.
• Lecture Notes 17c. Hierarchical Models III.
• Lecture Notes 18. Meta Analysis.
• Lecture 18 Paper. Using a Meta Analysis as a Prior.
• Lecture Notes 20. Meta Analysis.
• Lecture Notes 19. Bayesian Nonparametrics.
• Figure 1. Dirichlet Draws (YZ).
• Figure 2. Stick breaking (??).
• Figure 3. Chinese Restaurant Process. (YZ)
• Lecture Notes figs and tables. Meta Analysis 2.
• Covid-19 Prevalence in Santa Clara County Lecture Notes
  • Covid-19 Lecture Notes 1.
  • Covid-19 Lecture Notes 2.
  • Covid-19 Lecture Notes 3.
  • Covid-19 Figures.
  • Covid-19 Table.
• Selected Citations.

Wednesdays' Notes

• Please get latest versions from CCLE. #1 should be the same, but #2 was updated and is on CCLE. #3 only available from CCLE.
• Wednesday #1.
• Wednesday #2.
• Wednesday #3, see CCLE. Oct 13, talked about pages 1-8.
• Wednesday #4, Oct 20, continues from Wednesday #3, on page 9 to page 15.

Videos available on our CCLE page

• Lecture 01, Sept 27, 2021. Syllabus, Lecture notes 1.
• Lecture 02, Sept 27, 2021. Lecture notes 2, Wednesday notes #1.
• Lecture 03, Oct 04, 2021. Lecture notes 3, Lecture notes 4 (pages 1-15).
• Lecture 04, Oct 06, 2021. Lecture notes 4 page 16. Lecture notes 5 pages 1-13. Wednesday notes #2.
• Lecture 05, Oct 11, 2021. Lecture notes 5 pages 14 to end. Lecture notes 6 pages 1-15. Video not posted.
• Lecture 06 Oct 13, 2021. Lecture notes 6 pages 16 to end. Lecture 07 pages 1 to 9. Wednesday #3 pages 1-8, will continue next Wednesday. Posted. Only 2nd half of lecture was recorded.
• Lecture 07 Oct 18, 2021. Lecture notes 07 pages 10 to 15 (end). Lecture notes 08 all 1-12. Lecture notes 09 all, pages 1-4. (only recorded 2nd half of lecture, and mostly only sound almost no video)
• Lecture 08 Oct 20, 2021. Lecture notes 10 pages 1-15. Wednesday lecture: continued with #3, through page 16 top.
• Lecture 09 Oct 25, 2021. Finished Wednesday lecture #3. Lecture notes 11a pages 1-10.
• Lecture 10 Oct 27, 2021. Lecture notes 11a pages 10-11m Lecture notes 11b all. Wednesday lecture: Covid analysis, Lecture notes 1, 2, Figures all but last page.
• Lecture 11 Nov 01, 2021. Finished covid prevalence in Santa Clara County. Finished Lecture 12 pages 1-11. Started Lecture 13 pages 1-2 start page 3.
• Lecture 12 Nov 03, 2021. Finished lecture notes 13 pages 1-15, lecture notes 14a pages 1-13. Lecture notes 14b pages 1-3.
• Lecture 13 Nov 08, 2021. Student presentation schedule decided. Finished lecture notes 14b 3-6. Lecture notes 15 pages 1 to 29.
• Lecture 14 Nov 10, 2021. Lecture notes 15 pages 30 to 35; Convergence examples; Lecture notes 16a pages 1 to 10; Lecture notes 16b pages 1 to 5.
• Lecture 15 Nov 15, 2021. Lecture notes 16b pages 6 to 10, Lecture notes16c pages 1 to 14 end. Lecture notes 17a pages 1 to 8.
• Lecture 16 Nov 17, 2021. Lecture notes 17a pages 9 to 15, Lecture notes 17b pages 1 to 15.
• Lecture 17 Nov 22, 2021. Lecture notes 17b 16-20, lecture notes 17c 1 - 9. Talked about writing slides for talk.
•  

Homeworks

• To turn in homeworks, please email pdfs to Weiss, thanks.
• Homework 1.
• Homework 2.
• Homework 3.
• Homework 4.
• Homework 5.

2021 Homework Due Dates by 11:59pm.

• HW1: October 18
• HW2: October 25
• HW3: November 1
• HW4: November 15
• HW5: November 22
• Due dates can vary if needed.
• Associated report: Dec 6

2011 Notes: Bayesian Methods for Modeling Data

• BMMD.