Probabilities, Statistics and Computational Statistics

Written by Marc-Andre Seguin:marc

My background is in Jazz music, computer science and statistics. The first time I heard the word “actuary” was about 13 months ago. So, as you can see, I’m not a “real” actuary (yet) … and most of you are probably in the same situation. Although I’m not speaking from a standpoint of work-related experience, I would like to share my thoughts on the relevance of probabilities and statistics in the context of studying for (and passing!) actuarial exams.

I noticed that lots of students pursuing the actuarial career path are either getting their BSc. in “pure” mathematics or, coming from the other side of the fence, studying economics or social sciences. For the math-heads, the actuarial training seems more about getting the finance, the modeling and the applied stuff down (the logic and problem solving already being a big part of their trade) … while for econ people, the exams will usually push more on polishing their quantitative, analytical and problem solving expertise.

And this is exactly where I have an opinion: why not statistics?! It is a field that seems a bit orphaned, although increasingly popular because of recent advance in computer processing power. In my own experience, studying stats provides an excellent middle-ground in terms of applied versus abstract. First off, statistics starts with a dataset, which is very concrete in a way. Nevertheless, proofs in that field require the same scientific rigor as in mathematical analysis, geometry and algebra. So, in summary: my undergrad studies included a wealth of all the required math areas (same as the “pure” math students), but also allowed me to learn about all the interesting relevant applications: regression, experimental design, sampling and surveys, Bayesian stuff, etc.

Specifically, I took a 4th year undergrad class in modern computational statistics: I learned more about the real use of computers in data analysis in this class than in my whole degree! We saw rejection and importance sampling, Monte Carlo, Markov Chain Monte Carlo (MCMC), Bootstrap, permutation tests, applications of transformed random variables (finally!) and quite a few tricky proofs.

We even read actual research papers and presented our findings to the class and teacher. To my surprise, a fellow classmate discussed WINBugs for us (Bayesian Inference using Gibbs Sampling), an open-source software used daily by actuaries. It’s an application of MCMC and it is awesome how smoothly and nicely it can find estimators for the amount of tornados next season.

In closing, I also noticed that studying statistics made me find a use for all those coin-flipping exercises: all statistical results rely extensively on probabilities, and this, at all levels of study and research. Wasn’t it nice for me that my strongest subject in school was probabilities when I sat to write P/1? I’ll let you take a guess…

About the author: Marc-Andre (Larocque-) Seguin is the webmaster of and He confesses: “Actuarial science came as a bit of a revelation about a year ago. One of my teachers, a very kind and passionate top-dog researcher in probability, discussed the CERA program in his 3rd year undergrad probability class. Then followed my first visit to website and a few convincing conversations with classmates who had already passed 1 or 2 exams. You know the drill. [Laughs]”