MAST30001: Stochastic Modelling

2 assignments worth 20% of the final grade

Briefly about the subject
This subject talks about stochastic processes and how you can use them to model certain problems. The format of subject is quite standard: you’re taught certain concepts and then you’re given a problem which can be solved by modelling using the concepts you were taught. One could say it is the next step forward from MAST20004 Probability as there is a strong resemblance in the theme of the two courses.
Difficulty is the debatable part of the course. I reckon that it really comes down to just how much time you want to devote for this subject and your mathematics background. It is not a pure maths type of subject like Probability for Inference, Complex Analysis, etc so you don’t have to do (too much) analysis, mainly just calculations. However, the concepts are not easy to get your head around so I wouldn’t say that you could do well without spending a decent amount of effort, either.
Personally, I found this subject extremely difficult, possibly because of the little amount of time I devoted to it. It was very struggling for me to wrap my head around certain concepts. I'd always have to re-think about concepts that I thought I've already understood it. Honestly though, I find that probability subjects are difficult in general and need to be treated with respect if you wanna do well on it. This subject is certainly not for those looking for a chill third year maths subject.
My review will be pretty short as it’s not much different from MAST20004, MAST20005, MAST20006. If you’re looking into doing this subject, you’ve probably have done those and thus, you know what it was like.

Subject content
•Stuff that randomly change, one step at a time (Discrete time Markov Chain)
•Stuff that arrives over time but forgets what happened in the past (Poisson Process)
•Stuff that randomly change over time (Continuous time Markov Chain)
•Analysing queues of customers (Queuing theory)
•Stuff that arrives over time that remembers what happened in the past (Renewal Theory)
•Stuff that changes as a result of its fluctuations of its small constituents (Brownian motion)
Lecturer
Nathan is a cool dude. In lectures he seems a stoic and emotionless but then in tutorials he’s very enthusiastic and energetic. All I can say is that he is a very knowledgeable lecturer and he really understands this stuff. He’s also very generous when it comes to the exam. He is quite open about telling us what is to be expected on the exam and provides many past assignments and exams with solutions.

Lectures
•Lectures follow the usual format of a maths subject. You’ll find that Nathan’s lectures are kind of funny because everything he says, he makes it sound like it’s not important but really it is. He’ll often makes subtle jokes, but people don’t seem to catch those, probably due to his stoic expression.
•Nathan often spends time during lectures to summarise the stuff we’ve gone through and at the end of the semester, he even taught us how to study for the exam, something that seldomly happens at the tertiary education level.
Tutorial
•Tutorials follow the standard maths subjects format of working on the board together. The questions are either exam-style questions or walkthroughs to help you derive certain things, with the goal of assisting with your understanding of the material. I find these walkthrough questions to be extremely interesting and helpful.
•Tutorials are thankfully provided with solutions (unlike certain subjects).

Assignment
The assignment questions are on par with what you see in tutorials and what you’d expect on the exam. They’re pretty much just additional problems that can be a little lengthier but conceptually, it is just as difficult (or just as easy, depending on how you look at it).
I found the assignments very difficult, probably due to my lack of understanding of the subject.


Exam
The exam this year is quite fair, following a similar format to previous years’ exams:
•Discrete time Markov Chain (2 questions)
•Renewal Theory (1 question)
•Poisson Process (1 question)
•Queueing theory (1 question)
•Brownian motion (1 question)
In terms of difficulties, everything is quite standard, meaning that they’re just as difficult as previous years’ exams with certain exceptions. Queuing theory this year is a little bit easier but we were thrown with a very difficult Brownian motion question so it balances out. The difficult thing about this subject's exam is that only a few questions are standard in the sense that you've either seen it before in lectures or if you've really studied and understood the material, you'll be able to do it for sure. Lots of the questions are trick questions in the sense that they require you to come up with an ingenious idea to do it. In saying that though, all of this can be solved if more time is devoted to really understanding the material.
I haven’t gotten a chance to see my exam yet, but it seems like I lost 2 assignment marks (out of 20) and 12 exam marks (out of 80), putting myself at 86/100.

Yes, with screen capture etc.

Nathan Ross

Yes, lots with solutions.

5 Out of 5

3 lectures + 1 tutorial weekly

Semester 2 2019

wow, you gotta calm yo farm mate. Jk jk marks are discussed later, please keep reading

2x assignments (10% each), three-hour exam (80%)

This subject is a core unit for the Statistics and Stochastic Processes major, and an optional unit for Applied Mathematics. It's far more theoretical than you might expect a "modelling" subject to be, with plenty of formal definitions, theorems and proofs (although no need to produce any proofs in the exam or assignments). All of the examples in the tutorials and assignments were toy problems designed to illustrate the maths rather than realistically describe anything in the real world.

The basic principle of stochastic modelling is that you have a set of probabilistic rules describing how a system changes from one state to the next - similar to how ordinary differential equations provide rules for how a system evolves in time, but in a stochastic process, there is randomness involved. In this course we mostly looked at processes where the rules depend only on the current state of the system. These are called Markov chains (or Markov processes). We also focussed on systems where the state space was discrete, although possibly infinite.

For each kind of system covered in the course, we looked at long-run average behaviour (what is the chance of observing a system in a given state?) and the probability of particular events happening - for example, all servers being busy in a queuing system, or a gambler reaching a particular level of winnings before losing all of his money. There was a brief foray into Markov decision theory, which is about making decisions that affect the behaviour of a system in order to maximise some goal (the examples we saw were expected winnings in a game of chance, or expected profit in a house sale). I would have liked to have seen these ideas developed further!

Throughout the course, Nathan kept mentioning that to solve more interesting problems with these methods, you needed to do computer simulations. In light of this, I was disappointed that there was absolutely no computational aspect to this course.

The topics we covered were:
- discrete-time Markov chains (4 weeks)
- Markov decision theory (sadly, only one lecture)
- Poisson processes (1 week)
- continuous-time Markov chains (2 weeks)
- queuing theory (1 week)
- renewal theory (1 week)
- Brownian Motion (2 weeks)

Lectures: Nathan is very American, talks slowly, pronounces "zed" as "zee", and occasionally makes jokes - which is confusing, because he never sounds like he's joking. But he also explains concepts clearly, draws plenty of pictures and provides examples. The lectures go into more detail than what's written on the lecture slides; a typical lecture would cover 6–8 slides.

The worst aspect of the lectures was the timetabling: two at 9am and one at 4:15 on Friday afternoons! Lecture attendance had to compete with sleeping in and going to the pub, and since the lectures were recorded, I skipped almost a third of them. Apparently previous years have been similarly unpleasant and the draft timetable for 2015 has all of the lectures and the practice class at 9am.

Tutorials: I didn't go to a single one of the practice classes. This was a mistake, as when it came to study for the exam, I found that the tutorial problems had a variety of new and difficult problems on them and it would have been nice to have thought about them a bit earlier in semester.

Assessment: The two assignments were fairly simple, but like most maths subjects, the bulk of the assessment came from the exam. Tutorial problems and past exams are the best guide of what to expect, although this year's exam was longer and harder than I was anticipating (I think I only attempted 85% of it).

Yes, with screen capture for the document camera.

Dr Nathan Ross

Yes, from 2009, mostly with solutions.

4.5/5

The recommended text is "Elements of Stochastic Modelling" by K. Borovkov (one of the faculty members here at Melbourne). No need to buy it. Everything you need is in the lecture notes.

3x one-hour lectures, 1x one-hour practice class

2014, Semester 2

H1