Term Projects
Term Projects
A typical course will include one or two term projects. Below are some instances from recent years. Usually, projects are completed by teams of 4-5 students. A typed report is then submitted by the team, often created using the $\LaTeX$ type-setting system.
COVID-19 Vaccine Studies
Students explore statistical concepts from epidemiology, such as the relative risk (RR) ratio, vaccine efficacy and their estimators. Using contemporary (March 2021) data students evaluate confidence intervals for RR and discuss the interpretation. Media articles and misunderstandings in the popular press are also discussed, e.g., with regard to the (spurious) claim that certain vaccines were ineffective for older people.
Analysis of Package Contents
Students investigate the variation of food package contents and compare the observed variation with government regulations and testing procedures (which are based on an ISO standard and involve specific T-tests). The procedures are interpreted in terms of the underlying probability distributions.
Pseudorandom Numbers
Students investigate the notion of pseudorandom vs. random number generators. They choose either a generating process (e.g., linear congruential generators, middle square method, Rule 30 cellular automaton,…) and/or a verification procedure for randomness (Wald-Wolfowitz runs test, cumulative sums test,…) and present their topic in way comprehensible to their classmates (sophomore students with an introductory knowledge of probability).
Benford Distribution
The digits of numbers encountered in daily life don’t seem to follow a uniform distribution. Under certain common conditions, lower leading digits (1,2,…) will occur with greater frequency that higher digits (7,8,9). This fact, remarked on by Simon Newcomb in 1881, is related to scale invariance and unit invariance of the distribution and several attempts (some of which are erroneous) have been made to characterize and establish the distribution, which is named after Benford. Students investigate certain aspects based on historical sources as well as a contemporary publication by Berger and Hill.
Police Shootings in the United States
Using data gathered by the Washington Post, students analyze the rate of police shootings in the USA. Students verify conformity to a Poisson distribution (constant rate of shootings), check for dependence on weekdays and seasons, make predictions based on the Poisson distribution etc.
Photolitography Overlay
Based on a recent research publication and data provided by one of the authors (D. Djurdjanovic), students use multiple linear regression to fit the position of photolithography masks to the wafers that are being imprinted.
Fatal Traffic Accidents in Shanghai
Using data provided by the Shanghai Public Security Bureau, students analyze the rate of traffic accidents in Shanghai. Students verify conformity to a Poisson distribution (constant rate of accidents), check for dependence on weekdays and seasons, make predictions based on the Poisson distribution etc.
