### 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:**

Event | Time | Day | Room |
---|---|---|---|

Lecture | 1:00 - 2:50 | Monday | PH 61-262 |

Lecture | 1:00 - 2:50 | Wednesday | PH 61-262 |

Prof | Robert Weiss | robweiss@ucla.edu | |

Office Hours | 2:00 -- 2:50 | Tuesday | Online Zoom Meeting |

Office Hours | noon -- 12:50pm | Thursday | Online Zoom Meeting |

Week 10 | 1:00 -- 2:50pm | Monday Nov 29 | 5 Student Presentations |

Week 10 | 1:00 -- 2:50pm | Monday Dec 1 | 5 Student Presentations |

Finals Week | 11:30 -- 2:30pm | Monday Dec 6 | 5 Student Presentations |

Teaching Assistant | N/A | ||

Office Hours |

**General Information about Biostat 202C Bayes Theory**

- 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.
- In particular, exposure to likelihood theory and to completing the square in the normal likelihood will be extremely useful and is likely necessary.
- Mathematical background requires comfort with integration, differentiation, linear algebra and ugly algebraic manipulations.
- Grading is based on homework and projects.
- Course topics will include an overview of Bayesian theory, the mathematics underlying Bayesian methods, computation, the connection between conclusions and assumptions and data.
- The lectures are based on notes which will be made available on the web. The notes will be the primary reading material.

**Lecture Notes **

- 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
- 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.