MVE550 Stochastic processes and Bayesian inference Autumn 20
Course PM
This page contains the program of the course. Other information, such as learning outcomes, teachers, literature, examination, and old exams, are in a separate course PM.
Program
Work packages
The original schedule of the course is in TimeEdit but as the course is now given on-line, you should consult the schedule below.
On-line learning material for the course is structured into packages, with two packages each week. The packages contain
- recorded lectures
- overheads used in these lectures
- R code and other material used in these lectures
- references to relevant sections in our course literature
- lists of recommended exercises
- written solutions to some exercises
- recorded videos for solutions to some exercises
You are expected to go through and learn from this material BEFORE the on-line course meeting corresponding to each package. Thus there will be two Zoom course meetings each week, of roughly 45 minutes each, where we can all meet:
- You will be able to ask big and small questions related to the on-line learning material.
- You may ask me to review or clarify material. If you mail me questions on beforehand I can prepare, but this is not necessary.
- You may comment on or discuss course content or course organization.
- I will ask you some questions, to get feedback on what you know, and to help you understand what you need to know. (This will not be part of any grading).
- We can discuss whatever else we want to discuss in the whole group.
Exercise sessions
For each work package, some recommended exercises will be listed, although you are of course welcome to do other exercises as well. In addition to written answers/solutions and/or recorded video solutions being provided for some exercises, there will also be interactive Zoom sessions where you can ask questions about the exercises, and get help.
Assignments
An important part of the course are the three obligatory assignments. They should be solved and submitted in small groups of 2-3 students. The groups are created by the students themselves, go to "People" and "Groups". It may be a good idea to find a group directly, as you can then get started working together with somebody. To find group partners, you may go to "Discussions". For more details go to the list of assignments at the bottom of this page.
Office hours (CHANGED TIMES)
Petter Mostad will have "office hours" on Zoom, at times specified in the schedule below. Students can then get help and tutoring individually or in small groups. The office hours work as follows: You enter the "waiting room" of the zoom office by clicking on the link below. One student at a time is admitted from that waiting room, on a first-come first-served basis. Each student should limit their question time to about 10 minutes, if there is a line. The amount of office hours may be adjusted based on demand, but the preliminary plan is as follows:
Petter Mostad: Tuesdays and Thursdays 14:15-15:00. These times are different from during the first part of the course.
Piazza
We will try out using Piazza for class discussions. In this system, you may post your questions, even anonymously, and answer questions from other students. The course teachers will also look at and answer questions. Technical questions may be directed towards team@piazza.com.
Find our class signup link at: https://piazza.com/chalmers.se/fall2020/mve550
Lectures / work packages
| Contents | Study material | Zoom meetings |
|---|---|---|
| Introduction and review |
Lecture 1: video1.1 video1.2 / overheads Dobrow Chapter 1 + Appendices A, B, C, D Exercises: Dobrow Chapter 1: 6, 9, 10, 14, 16, 20, 24, 30, 32, 35 . Answers to these exercises to Chapter 1 Dobrow can be found here Recorded solutions: Tuesday Exercise: For the exercise session I will demonstrate exercise 1.20a and answer questions. Video of first Exercise Session Thursday Exercise: I will mainly answer questions and not demonstrate any exercise. No recording of this session as it was mainly devoted to questions. |
Course meeting Tuesday 3/11 13:15-14:00 Exercise session Tuesday 3/11 15:15 - 16:00 Exercise session Thursday 5/11 15:15-16:00 Password for all meetings: 135791 |
| Basics of Bayesian inference |
Lecture 2: Video2.1 video2.2 overheads / R code Compendium Chapter 1 (now includes solutions to exercises) Exercises: Compendium Chapter 1: 3, 4, 6, 7, 8, (9, 10). The compendium will be updated Wednesday 11/11 with an Appendix containing exercise solutions. For the exercise session I will demonstrate exercise 1.11 in the Compendium and then it is a question session. Recorded video of the exercise session can be found here Link Recorded solutions: Exercise C_1_3_a, Exercise C_1_3_b, Exercise C_1_3_c (I realised that I did not mention that you can solve c faster by using the formula (k+1)/(n+2) from the Compendium page 6. I used a more general solution method which will work on other problems as well.) |
Course meeting Thursday 5/11 13:15-14:00 video (from last part of meeting) Exercise session Tuesday 10/11 15:15-16:00 Password: 135791 |
| Markov chains |
Lecture 3: video3.1 video3.2 / overheads / R code Dobrow Chapters 2 and 3 Exercise session: I will demonstrate exercise 2.14 in Dobrow and after that it will be a question session. The recorded exercise session can be found here Exercises: Dobrow Chapter 2: 2, 7, 10, 14, 16 17, 18 20, 21, 22, 26. Answers can be found here Recorded Solutions: Exercise 2.1 Exercise 2.11 (I realised that my notation on 2.11 might not have been too clear with Bin(n, p). What I meant is just that for each entry in the matrix you take the probability from a Binomial distribution with parameters n and p. If there are questions or if something is unclear then you can email me / Anton) |
Course meeting Tuesday 10/11 13:15-14:00 Exercise session Thursday 12/11 15:15-16:00 Password: 135791 |
| Markov chains |
Lecture 4: video4.1 video4.2 / overheads Dobrow Chapter 3 Exercises: Dobrow Chapter 3: 2, 5, 9, 14, 18, 22, 30, 35, 38, 41, 46, 64. Answers can be found here For the exercise session I will demonstrate exercise 3.54 in Dobrow. The recorded exercise session can be found here |
Course meeting Thursday 12/11 13:15-14:00 Exercise session Tuesday 17/11 15:15-16:00 Password: 135791 |
| Hidden Markov Models (HMM), inference |
Lecture 5: video5.1 video5.2 / overheads Compendium Chapters 2 and 3, now updated with answers to exercises chapter 3. Exercises: Questions 1, 2, 3, 6 from Compendium chapter 3. For the exercise session I will just have a question session and not demonstrate any exercises. Recorded solutions: C_2_3_a, C_2_3_b, C_2_3_c, C_2_3_d, C_2_3_e, C_2_3_f |
Course meeting Tuesday 17/11 13:15-14:00 Exercise session Thursday 19/11 15:15-16:00 Password: 135791 |
| Branching processes |
Lecture 6: video6.1 video6.2 / overheads Dobrow Chapter 4. Questions for breakout rooms Exercises: Dobrow Chapter 4: 2, 5, 6, 8, 12, 19, 20, 26, 29 For the exercise sesson I will demonstrate exercise 4.28 in Dobrow and then it will be some time for questions. The recorded exercise session can be found here. (I got a question regarding exercise 4.6 and I just wanted to expand a little bit on the answer. The key idea is that we want to use the independence of X_i so that we can split the expectation in the definition of the generating function into a product of expectations. This can only be done if we know the upper limit of the sum, thus we need to condition on it through either the towering property of the expected value, or by using the law of total expectation.) |
Course meeting Thursday 19/11 13:15-14:00 Exercise session Tuesday 24/11 15:15-16:00 Password: 135791 |
| Markov chain Monte Carlo (MCMC) |
Lecture 7: video7.1 video7.2 / overheads / Rcode Dobrow Chapter 5 Exercises: Dobrow Chapter 5: 2, 4, 5, 6, 8 For the exercise session I will demonstrate exercise 5.19. Recorded videos for the exercise session can be found here: Part 1 Part 2 Recorded solutions: 5.8 |
Course meeting Tuesday 24/11 13:15-14:00 Exercise session Thursday 26/11 15:15-16:00 Password: 135791 |
| Inference for branching processes, MCMC for inference |
Lecture 8: video8.1 video8.2 / overheads / Rcode Exercises: Dobrow Chapter 5: 9, 17, 18 For the exercise session I will only have a question session. For a recorded solution of an exercise then I recommend that you look at the two videos from the last exercise session. |
QUESTIONS FOR BREAKOUT ROOMS / answers Course meeting Thursday 26/11 13:15-15:00 Exercise session Tuesday 1/12 15:15-16:00 Password: 135791 |
| Poisson processes |
Lecture 9: video9.1 video9.2 NOTE: I FORGOT TO SHARE THE WHITEBOARDS IN LECTURE 9.2. YOU MAY SEE THEM HERE: Whiteboard1 Whiteboard2 Whiteboard3/ overheads / Rcode Dobrow Chapter 6 Exercises: Dobrow Chapter 6: 2, 5, 8, 10, 14, 16, 21, 24 For the exercise session I will demonstrate exercise 6.21 and then it will be some time for questions. The exercise session can be viewed here Recorded solutions: 6.8 |
Course meeting Tuesday 1/12 13:15-14:00 In addition to answering any question about any subject, I will give a short summary, go through EXAM 2019-01-16 q6, and questions 6.32 and 6.44 from Dobrow. There will be no breakout rooms :-) The whole meeting will be recorded. video from meeting / R code shown in meeting Exercise session Thursday 3/12 15:15-16:00 Password: 135791 |
| Continuous-time Markov chains |
Lecture 10: video10.1 video10.2 / overheads / Rcode Dobrow Chapter 7 Exercises: Dobrow Chapter 7: 1, 4, 5, 6, 12, 14 Recorded solutions: 7.4 , 7.12 . For the exercise session I will only answers questions and not demonstrate any exercises. |
Course meeting Thursday 3/12 13:15-14:00 In addition to answering any question about any subject, I will give a short summary, go through EXAM 2020-04-08 q5 and EXAM 2019-08-19 q6. There will be no breakout rooms. The whole meeting will be recorded. Exercise session Tuesday 8/12 15:15-16:00 Password: 135791 |
| Continuous-time Markov chains |
Lecture 11: video11.1 video11.2 / overheads / Rcode Dobrow Chapter 7 Exercises: Dobrow Chapter 7: 18, 20, 23, 26, 30, 34, 39 Recorded solutions: 7.18, 7.36 For the exercise session I will demonstrate Exercise 7.20 and 7.30. Unfortunately it appears Zoom could not save the recorded video for the exercise session. I will see if I can rerecord the solutions. |
Course meeting Tuesday 8/12 13:15-14:00 In addition to answering any question about any subject, I will give a short summary, go through EXAM 2019-01-16 q7 and EXAM 2019-08-19 q7. There will be no breakout rooms. The whole meeting will be recorded. Exercise session Thursday 10/12 15:15-16:00 Password: 135791 |
| Brownian motion |
Lecture 12: video12.1 video12.2 / overheads / Rcode Dobrow Chapter 8 Exercises: Dobrow Chapter 8: 1, 2, 6, 9, 16, 18 Recorded solutions: 8.2 Exercise session can be found here |
Course meeting Thursday 10/12 13:15-14:00 I will give a short summary and go through EXAM 2020-01-18 q7 and EXAM 2019-04-24 q8 Exercise session Tuesday 15/12 15:15-16:00 Password: 135791 |
| Brownian motion |
Lecture 13: video13.1 video13.2 / overheads / Rcode Dobrow Chapter 8 Exercises: Dobrow Chapter 8: 19, 22, 25, 26, 29 Written solutions to these exercises. For the exercise session I will demonstrate some exercises problems (10-15 min) and then it will be time for questions. |
Course meeting Tuesday 15/12 13:15-14:00 Exercise session Thursday 17/12 15:15-16:00 Password: 135791 |
| Review |
Lecture 14: video14.1 video14.2 video14.3 / overheads Review. Exam tips. |
Course meeting Thursday 17/12 13:15-14:00 Password: 135791 |
Answers to exercises: Click here
The following sections of Dobrow are NOT part of the curriculum: 3.9, 3.10, 5.5, 5.6, 6.8, 9.1,9.2,9.3.
Course summary:
| Date | Details | Due |
|---|---|---|