MAST90082: Mathematical Statistics

2 assignments worth 10% each and 1 exam worth 80%

This is a relatively relaxing subject at Master level and there is a legitimate reason for this: it is attempting to accommodate students from different backgrounds like say, Economics, Finance, Mathematics, etc. As a result, the rigour level is kept to a minimum and the pace is fair, meaning that the amount of content is also fair and that's what I meant by "relaxing" - relaxing in terms of amount of content, pace and abstractness. My view is that if you are someone who wants a chill subject, or a Maths students with interest in Statistics or a student from a different background wanting to do a Maths subject, you should definitely give this a go.

To sum it up, this subject is, in my opinion, a sequel to MAST20005 Statistics in the sense that it revisits topics MAST20005 Statistics and explore them a little further but also doesn't go too deep in any topics. The "atmostphere" and "flavour" of the subject also resembles MAST20005 Statistics, not too much pressure (like say MAST20004 Probability or MAST30020 Probability for Inference).

As for the content the subject is divided into 3 major parts

1. Point estimators
2. Hypothesis testing
3. Interval estimators

For topic 1, the first 7 weeks, the set up is that we want to estimate certain quantities (say the average amount of money Australians make per day) and so we collect data and using those datas, we compute some figures. The questions one can ask are:

• How should we compute these figures (What estimators to use? MME or MLE?)
• What properties do these figures possess (Properties of MME and MLE)
• How do we compare which figures are better? (Evaluating estimators)

So the topics covered were
- Method of moment and maximum likelihood estimators
- Bias, mean square error
- Uniformly minimal variance unbiased estimators (UMVUE)
- Crame-Rao lower bound
- Exponential family
- Sufficiency, completeness and ancillary statistics
- Rao-Blackwell and Lehmann-Scheffe Theorem
- Decision theory and Bayes estimators
- Asymptotic estimators

For topic 2, the next 2 weeks or so, the set up is that we now have a claimed figure for our quantity of interest. Should we trust that figure? How can we test the claim? The natural questions one can ask (and thus, try to answer) are

• Which tests are good?
• Can we find a best test?

The topics covered were
- Uniformly most powerful test
- Likelihood ratio test
- Bayes test

For topic 3, the set up is that although getting a figure for estimating our quantity of interest is nice, we don't know how sure we can be of such a figure. It might be instead nicer to get a range of values where we think our quantity lie in. But how do we find such an interval? How does changing the length of such an interval change our confidence level?
The topics covered were
- Inverting tests
- Pivoting the CDF
- Bayes intervals

So the topics covered were more advanced than MAST20005 for sure, but the depth and rigor was kept low, which according to the lecturer, was kept low to accommodate students from various backgrounds.

Mathematics and Statistics

Yes, with screen capture etc.

Liuhua Peng

Yes, there was a mock exam which is a past exam

4.5 Out of 5

The course is based on the book Statistical Inference by Casella and Berger but you don't really need it. The lecture notes are self-contained.

3 lectures a week and surprisingly no tutorials

2021

Haven't received it yet