Two Approaches to the Initial Transient Problem

P. W. Glynn

Monte Carlo and Quasi-MonteCarlo Methods in Scientific Computing[H. Niederreiter, P. Shuie, eds.] Lecture Notes in Statistics, Vol. 106, Springer-Verlag, New York, 49-57 (1995)

This paper describes two different approaches to dealing with the initial transient problem. In the first approach, the length of the "warm-up period" is determined by obtaining analytical estimates on the rate of convergence to stationarity. Specifically, we obtain an upper bound on the "second eigenvalue" of the transition matrix of a Markov chain, thereby providing one with a theoretical device that potentially can give estimates of the desired form. The second approach is data-driven, and involves using observed data from the simulation to determine an estimate of the "warm-up period". For the method we study, we are able to use a coupling argument to establish a number of important theoretical properties of the algorithm.