Part 2: Case Study Competition

A lot of applied statistical techniques are best learned by doing, such as experimental design, predictive modelling, simulation, etc. Probability models (what is covered in STAT 334) are often fairly theoretical, but STAT 334 is a course for business and accounting students, who are more interested in the applications. They are also familiar with the idea of case studies from the business courses they take.

Because of that, I decided to have a Case Study Competition in STAT 334. The choice of topic was completely up to the students (in groups of 3) and they had to take something of interest to their group and model it with a Markov Chain. The competition involved in-class presentations to their peers and a panel of judges, and a written report due after seeing all the presentations, so they could incorporate the judges' feedback and ideas from their fellow classmates. I also had them write a short reflective paper on what they learned from their own project and had them give some critique of 2/3 other groups' projects.

The competition went really well. It was well worth a week of class time to do the presentations, since we saw a huge variety of topics chosen by the students themselves, and many of the course concepts applied in various ways. The judges (other faculty in my department) were very impressed with what the students were able to do with the material after a fairly quick introduction. The funding from the LITE grant mostly went to cash prizes for the competition.

Through the process of choosing the topic, seeking out data sources, creating the transition matrix itself from the data, and then doing the analysis appropriate for their topic, the students gained a much better appreciation for the versatility of the Markov Chain model, as well as recognizing its limitations. Building the model themselves rather than starting from a model handed to them is essential to understanding how it works.

There were too many excellent topics to list them all, but I want to briefly highlight a few:

• Music - analyse music of different styles and then use the resulting chains to simulate music from each of the styles.
• Election results - using the last several Canadian elections, predict whether the incumbent party will win their seat.
• HIV/AIDS progression - predict the white blood cell count of a patient receiving treatment for HIV at 18-month intervals.
• Roulette - determine the optimal betting strategy when playing roulette, and see how long it takes to go bankrupt.
• Genetics - given genotype information of two parents, model the genotype of their offspring
• Hockey/Basketball/Soccer (more than one group looked at this topic in different ways) - predict the performance of a team based on past performance, and see if "winning streaks" or "losing streaks" are statistically significant.
• Weather (again, more than one group looked at this topic) - predict rainfall/snowfall/weather based on the last few years/days information.
• Stocks/Bonds - predict change in bond rating (AAA, AA, etc) of a company, or the % change in monthly t-bill rates.

Overall the students gained a lot of experience and knowledge both from their own project and observing each others' projects. As one of the students wrote in their reflective paper, "The application of Markov Chains in our real life problems allowed us, as a class, to see the very appropriate application of one simple statistical concept in a kaleidoscope of areas in the world we live in today. The experience to me was one of the first, which I felt strengthened my conviction on the application of Math in everyday life."

As a teacher, I can't ask for a better result than that!