Nothing goes to infinity in real data: Assessing distances between probability distributions

A key result in classical probability and statistics is the Central Limit Theorem, asserting asymptotic normality under conditions on the underlying distribution of observations. The limit is taken as the number of observations tends to infinity, but real data are finite. Hence explicit bounds on the distance between the object of interest and the limiting distribution are required to account for the approximation error. A method which has proven useful for obtaining such explicit bounds in rather general situations, which may include complex dependence, is Stein's method. This talk will give a very brief introduction into Stein's method and then illustrate it with an explicit bounds on an approximation of exponential random graphs.