Live/In-person session diary 2023

General information

We may attempt to live stream, the live in-person sessions. Please note that it is UCL’s expectation that students attend in-person. The Zoom link is available here. Not all sessions will be recorded or streamed. The recording links will be available on Moodle.

By UCL week

Week 6

• First meeting: introductions, module outline and mechanics
• We discussed the basics of rejection sampling
• We proved the weak law of large numbers and discussed various forms of convergence
• This meeting was recorded can the link to access this is available only on Moodle

Week 7

• We discussed the homework from last week and introduced the concept of coupling.
• Worksheet
  • Partial Solutions

Week 8

• We discussed the relation between uniform random variables, coin flips, and the inverse transform method.

• We discussed coupling in more detail and its relation with the total variational distance.

• We introduced Markov chains, and the key assumption of them being aperiodic and irreducible

• Worksheet

  • Partial solutions

Week 9

• We discussed Poisson processes
  • Shiny App
    • Source
• Worksheet
  • Solutions

Week 10

• We discussed ICA1 expectations and guidelines.
  • We went over ICA1 2022
• We discussed and coded a simple voting model. More in-depth information and background can be found here or here.
  • Worksheet and solutions

Week 11

• we discussed the content delivery and ethos of the module.

• We reviewed continuous-time Markov chains.

• Worksheet

  • Solutions

Week 12

• We discussed expectations for ICA1
• We reviewed the worksheets on MCMC and Voroni cells
• We introduced a renewal-type argument for Markov chains

Week 13

• We reviewed convolutions and introduced some ideas in renewal theory, including Excessive life and stationary increments
• Worksheet

Week 14

• We discussed the two versions of Little’s theorem.
• Worksheet
  • Partial solutions

week 15

• We released ICA2
• We discussed solutions to ICA1 (solutions on Moodle only)
• We went over some key results for \(M/M/1\) queues

Week 16

• ICA3 will be released soon
• We gave an overview of the module
• We introduced C++
• We discussed the Week 14 worksheet

Other notes

• ICA1: Released 03/11/2023; Due 17/11/2023
• ICA2: Released 08/12/2023; Due 01/03/2024
• ICA3: Released 15/12/2022; Due 09/02/2024

Version: 12 December 2023