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 com​mu​nity​.monash​.edu/​m​axima

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

DLMF

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

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

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.