Proposal for summer course in Cortona : Introduction to distribution approximations and Stein’s method

A large number of applications in probability, statistics, biology, mathematical physics, computer science, and many other areas rely on approximations of distributions based on limiting results as a parameter, often a sample size, tends to infinity. The best known example is surely the Central Limit Theorem (CLT), which is used to justify the normal approximation in many contexts. A companion Poisson ‘law of small numbers’ is perhaps of no lesser importance. Recently, techniques such as Stein’s method have become available that allow one to compute a bound on the error when making such approximations. Of particular interest are situations where one cannot assume independent identically distributed random variables, as in the standard CLT. In this case the bounds on the approximation depend on the sample size, and on characteristics of the dependence. The scope of applications is wide and has been rapidly growing in recent years, including molecular sequence analysis, high