What is statistics?
Professor Sean van der Merwe
What is statistics?
“Statistics is the grammar of science.”
- A statistic is just a summary of some numbers
- So statistics starts with describing patterns in numbers
- But numbers are never certain nor exact
- So statistics is really about understanding uncertainty
Solving scientific problems
Statisticians get to help with every step!
Maths as foundation
- In our department we do not do maths for the sake of maths (the Maths department does that)
- We do maths because it is the foundation of so much more
- Actuarial Science is built on Mathematical Statistics
- Mathematical Statistics is built on Mathematics
Examples
Let’s shuffle a deck of cards
deck <- paste( c(2:10, 'Jack', 'Queen', 'King', 'Ace') |> rep(times=4), 'of',
c('Spades','Diamonds','Clubs','Hearts') |> rep(each=13) )
# To draw a hand of 7 cards:
hand <- deck |> sample(7)
# Shuffling is taking a sample the same size (52) without replacement:
shuffled_deck <- deck |> sample(length(deck))
# To do a bootstrap sample just add: , TRUEText information
Perhaps we shall summarise the complete works of Shakespeare in a word cloud?
Survey exploration
What about business?
We could simulate a pair of \(VARIMA_2(1,1,1)-tGARCH(1,1)\) financial time series like so:
Trying to get your grandparents to take their pills
Pollution at a dam
Bacterial growth on boerewors
\[g(t)=a e^{-b e^{-ct}}+\varepsilon_t,\ f(\varepsilon)=\frac{\Gamma(0.5(\nu+1))}{\sqrt{\pi\nu}\Gamma(0.5\nu)}\left(1+\frac{\varepsilon^2}{\nu}\right)^{-0.5(\nu+1)}\]
Careers
- Career options: Actuary, data scientist, statistician, economist, marketing strategist, banker, risk analyst, …
- Employers: Banks, insurance, investment companies, clinical research organisations, marketing companies, …
- UFS options: Actuarial Science, Mathematical Statistics + economics or psychology, Statistics + accounting or biology, Data Science (programming + mathematical statistics), Risk analysis (not the same as risk management), Microbiology + statistics, …
Begin with the end goal in mind and do what it takes to get there.
Be real though
- Actuarial Science is difficult, much more difficult than medicine
- It takes a minimum of 8 years to become an actuary: 4 to 6 years of studying at university and another 4 to 20 years of studying while working
- Only a tiny fraction of people make it all the way.
- There are great alternatives though: people starting in actuarial science or something close to it almost always end up getting a good degree, a good honours degree, and rewarding work!
- Some are actuaries, some are data scientists, some are statisticians or statistical programmers, some are in business, marketing, banking, etc.
Why the University of the Free State?
- We have many actuaries available to you in person, more than any other university in SA!
- All students who finish any honours degrees I’ve mentioned end up well employed!
- A productive study environment
- A decades long track record of success
“I’ve forgotten what you just said.”
Just remember one of these:
Young stars