Gilles Stoltz’s abstract

Statistics is a field of mathematics that studies the numbers that surround us or that are obtained from scientific experiments. These numbers are modeled as realizations of random variables and mathematical studies can then link the the numbers collected (i.e., the sample behavior) to the hidden truth (i.e., the population behavior). We will explain in detail these sample-to-population generalizations, which correspond to what is referred to as a statistical model. We will hint at the rich theories of confidence intervals, statistical hypothesis testing, and linear regression. We will illustrate the theory by numerical experiments in lab sessions. And of course, we will constantly discuss real data-sets and explain what conclusions may be (or cannot be) drawn from them. Examples of such data sets include: the use of Benford’s law to detect manipulations in accounts; the historical study of fathers’ and sons’ heights by Galton; the experiments by Mendel to prove his theory of randomized association of genes; etc.