The present set of lecture notes are prepared for the course “Statistik 2” at the University of Copenhagen. It is a revised version of notes prepared in connection with a series of lectures at the Swedish summerschool in Särö, June 11–17, 1979. The notes do by no means give a complete account of the theory of contingency tables. They are based on the idea that the graph theoretic methods in Darroch, Lauritzen and Speed (1978) can be used directly to develop this theory and, hopefully, with some pedagogical advantages. My thanks are due to the audience at the Swedish summerschool for patiently listening to the first version of these lectures, to Joseph Verducci, Stanford, who read the manuscript and suggested many improvements and corrections, and to Ursula Hansen, who typed the manuscript.

with the usual ±1 reinforcement signal. We consider the scenario in which the goal of the game, rather than just winning, is to maximize the number of wins in an allotted period of time (or maximize the expected reward in the same period). In the reinforcement learning literature, this type of tradeoff is often handled by tuning the discount parameter in order to encourage the learning algorithm to find policies that take fewer steps on average, at the cost of a lower probability of winning. We show that this approach is not guaranteed to solve the tradeoff problem optimally, and hence a different strategy is needed when tackling this type of problems. I.

A central limit theorem for random walk in random environment on marked Galton-Watson trees