This module will assume some experience with the basics of probability and statistics, and Markov chains from UCL Stat0007. We will make extensive use the software program R and Python. No prior experience with Python will be assumed, and usually you will be offered a choice between R or Python.
Quick review of probability and statistics from the perspective of R and Python.
Markov chains: convergence to stationarity, Doeblin coupling, coupling from the past, Markov chain Monte Carlo.
Point process: Poisson processes, spatial Poisson point processes, Continuous-time Markov chains, semi-Markov processes.
Renewel theory: renewal theorems, Little’s theorem.
Queues: stationary distributions, blow-up, waiting times.
We will have 3 ICAs. Pay no attention to the ordering of ICA 2 and ICA 3.
The first ICA (30 %) will be a regular assignment given around the middle of the term to make sure we have learned the basics.
The third ICA (30 %) will be centered around more involved problems that will require a synthesis of ideas from throughout the module. This may be done in groups. Due in 2024
The second ICA (40 %) will be a group project based using the knowledge learned throughout the course. Due in 2024. Some examples include:
The ICAs will have a coding component that would need to be done in R or Python. Assignments are to be typeset, in a favour of Markdown/Latex, using RMarkdown (or Quatro) or Juptyer notebook.
Throughout the module students will have the chance to work on various exercises that will test and build their understanding of the material.
As per UCL guidance, on accessibility, most materials will be provided in html format. Source files will usually be made available, and it is possible to generate pdf files from these source files; another way to generate pdf is to as a print-as-pdf option.