Welcome to the revised STAT3004/STAT7304 Probability Models & Stochastic Processes at The University of Queensland. The course is currently coordinated by A/Prof Yoni Nazarathy. The tutors are Evan Jasiewicz and Jack Thompson. At the time of preparing this page, we are in the early days of the Covid19 crisis. There were classes for 3 weeks at which point we paused for a week. Now after the pause, classes continue on March 23 in online mode with 10 weeks of semester remaining. These are interesting and challenging times. But we can do it!
The first three weeks prior to the pause focused on the simple branching process, very basic properties of simple random walks, the gambler's ruin example, and a basic introduction to discrete time Markov chains, including the computation of n-step transition probabilities via diagonalization of the transition probability matrix for computing matrix powers. You can view these lectures (9 in total) on blackboard (Feb 25, 2020 - March 13, 2020).
Now in the remainder of the course, we will continue to study discrete time Markov chains, quickly moving onto continuous time Markov chains. Our overarching aim will be to get a good grasp of Markov chains so we can analyze the stochastic SIR epidemic model (Susceptible - Infective - Removed). This model appears to be very relevant for our current Covid19 situation, hence there is strong motivation to study it.
Let's not be confused, we won't save the world by carrying out the assesement for this course, but since unfortunately we are surrounded by this "motivating" example, integrating it in the course may help us stay focused and motivated. We may also come out of this with background that can help contribute to the many research groups that are forming around Covid19 (and the potential second or third wave that may appear in the months and years to come).
Our progression through the material will be somewhat similar to the previous offering of the course, however we will accelerate at certain points, and slow down at others, keeping in mind that our main goal is to be able to use stochastic processes as epidemic models. There will also be a bit more computation and simulation involved and this will be reflected in the assessment (see details about the assessment items below). Note that students that have taken this course with a view of gaining expertise in finance, operations research, theoretical probability, or other fields will still gain experience and knowledge through the study. However, the measure theoretic part (which was originally planned to take several weeks in the second half of the course), will only be skimmed.
While YouTube videos and Zoom sessions will be available, in this revised format, information from books will be the central pillar of study. For this there is a clear list of four resources below. These are four books that we abbreviate via [SP], [MC], [EM], and [SWJ]. The books [SP], [MC], and [EM] are available in the library for UQ students. The [SWJ] book has an online draft that is available. For each of these books we have highlighted a few chapters that constitute the relevant material or review. That is 12 chapters in total. Parts of these chapters will serve as the bulk of the material for the course and others will only play a supporting role.
There will be some focus on computation and experimentation. For this the [SWJ] book demonstrates how to do this via the Julia language. You can use Julia as has been done in the video lectures, but you are not required to. Instead you can use, Python, R, Matlab, or any other tool you see fit.
Here is the self study guide.
Here is a YouTube playlist containing some of the lecture recordings (from week 4 onwards). The recordings of weeks 1-3 are on blackboard.
There are also further suggestions via blackboard messages. In addition Piazza can be used for communication. The general theme is to carry out self reading of content from the chapters above, together with individual work on the projects and problem set.
The first two components of the assessment are projects that require some problem solving skills, some programming, and some creativity in presentation. The second two components are of the more classic "maths problem" form where the problem set should serve as some preparation for the exam.