Statistical politicians

Last week we had the pleasure of Professor Stephen Pollock (University of Leicester) visiting our Department, best known in academic circles for his work on time series filtering (see his papers, and his excellent book). But he has another career as a member of the UK House of Lords (under the name Viscount Hanworth — he is a hereditary peer).

It made me wonder how many other politicians have PhDs (or equivalent) in statistics, or at least in mathematics. I realise that a lot of mathematicians before the 20th century were often involved in politics, in one way or another, especially in France. Also, the notion of a PhD is a relatively recent invention. But if we restrict the time to 1950 onwards, there must be quite a few politicians with doctorates in the mathematical sciences. Continue reading →

Three jobs at Monash

We are currently advertising for three academic positions, suitable for recent PhD graduates.

Lecturer (Applied Statistics or Operations Research)

Lecturer (Econometrics/Business Statistics)

Please don’t send any questions to me. Click the “More information” links and follow the instructions.

MAXIMA research centre at Monash Uni

The “Monash Academy for Cross and Interdisciplinary Mathematical Applications” (MAXIMA) is a new research centre that aims to maximise the potential of mathematics to deliver impact to society. It will be led by Kate Smith-Miles. I will also be involved along with several other mathematicians at Monash. Our mission at MAXIMA is to find solutions to 21st century problems by dismantling mathematical barriers.

MAXIMA will be launched on 25 September at a public lecture on “The Role of Embedded Optimization in Smart Systems and Products”.

More details at

Advice to PhD applicants

For students who are interested in doing a PhD at Monash under my supervision.

First, read the instructions on how to apply.

Second, poke around my website to see the sorts of topics I work on. There’s no point asking to do a PhD with me if you want to do research on something I don’t know much about. In particular, please note that I’m not really interested in finance or economics. There are some excellent researchers at Monash on both topics, but I’m not one of them.

If you’re still interested, here is what I normally expect. You should have a strong background in statistics or econometrics (at least honours or Masters level) along with some mathematics and computing. It is essential that you have studied some matrix algebra, multivariate calculus and optimization. You should be capable of programming with a high level language such as R or Matlab; if you can write in C as well, even better.

Students who struggle either find they don’t know enough mathematics (or didn’t pay attention when they learned it), or they don’t know enough computing. I don’t expect students to be whiz programmers, but I do expect them to know about for loops, if statements, local variables and functions, and I assume they have some idea about nonlinear optimization.

I do not expect that you have studied specific topics close to my research such as time series analysis, forecasting, nonparametric smoothing, etc. If you have a solid background in statistics and mathematics, then you’ll pick up the necessary material easily enough.

Much of the first year of a PhD is spent in reading the relevant background literature and developing some necessary research skills. Most students have not produced anything publishable after one year, but they will usually have developed good research skills, have read a lot of papers and will be ready to start doing some research of their own.

I expect all my PhD students to have read all of the archives of this blog (even the jokes page) and to subscribe to new posts. The primary purpose of the blog is to discuss research issues that students working with me should know about.

Most students will need a scholarship. Applications for PhD scholarships at Monash close on 31 October each year. Check out the instructions for scholarship applications. Scholarships are highly competitive and we receive many applications from students around the world. You would normally need first class honours from an excellent university to be in the running for a scholarship. International students will also need to have satisfied the English language requirements.

If you’re thinking of applying in the next round, use the time between now and then to prepare — learn R, revise your mathematics, read some research papers, and prepare a research proposal.

Online mathematical resources


For nearly 50 years, a standard reference in mathematical work has been Abramowitz and Stegun’s (1964) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. It has provided a marvellous collection of results and tables that have been indispensable for a generation of mathematicians. I’ve used it to look up computationally efficient methods for calculating Bessel functions or gamma functions, or to find one of those trigonometric identities I learned in high school and no longer remember. Apparently nearly 1 million copies of the handbook have been printed and it has also been scanned and put online.

Lately, the handbook has fallen out of favour a little, partly because there is not such a need for it. We no longer need tables for trigonometric functions or logarithms, and a lot of functions are built into R, including Bessel functions and variations on the gamma function. Another reason for its declining popularity has been the rise of online resources: if you want to know something about orthogonal polynomials, there is a good chance it is covered in the Wikipedia article.

Now the handbook has been reissued as the NIST Handbook of Mathematical Functions (Cambridge University Press) with a free web edition called the NIST Digital Library of Mathematical Functions (DLMF). It has been updated to include colour graphics, pointers to recommended software, and lots of new topics to reflect work from the last 50 years.


WolframAlpha is now a year old and it has become a remarkable resource for some things. It was originally compared to Google which is inappropriate — they are intended for different purposes. Google indexes the web, while WolframAlpha is a knowledge engine.

Recently I needed to find the integral of 2\tan(2x)\sec^6(2x). Typing integral 2tan(2x)sec^6(2x) gave me the result straight away. Of course, I could use Mathematica or Maple for this, but it is much easier to use my browser. It also means such algebraic results are available to everyone without needing specialist symbolic algebra software.

A few days later, I was working on a project involving modelling electricity demand as a function of temperature. The temperature data looked odd and I suspected it was all out by one day. To check, I typed melbourne temperature 21 February 2010 into WolframAlpha and it promptly gave me the temperature data for Melbourne Airport for that day, and with one more click of the mouse I had the data for the whole week, confirming my suspicion.

For the sorts of things that WolframAlpha is good at, see the examples page.


Wikipedia needs no introduction and it is surprisingly good in some areas of mathematics (e.g., probability distributions) but not very good for some areas of statistics (e.g., see the article on ARIMA models or the one on Cronbach’s alpha). The good news is that the statistics articles are improving and is now starting to be usable as a first port of call when looking up an unfamiliar method.