The problem of the initial transient (again), or why MSER works

In a comprehensive study of methods for mitigating the problem of the initial transient, Hoad et al (2009) conclude that MSER (White, 1997) is an efficient, effective, and robust truncation rule, appropriate for automation. Franklin and White (2008) suggest that MSER works because it minimizes an approximation to the mean-squared error in the estimated steady-state mean; Franklin et al (2009) offer empirical support for this suggestion. In this paper, we use the example of an M/M/1 queue to provide a clear restatement of initialization problem in both the time and frequency domains, distinguishing between the biasing effects of initialization and autocorrelation. We demonstrate that mitigating initialization bias is not a matter of determining the most representative initial condition per se and that minimum mean-squared error is a more appropriate objective. This demonstration also argues against the efficiency of the replication/deletion approach to output analysis.