Statistical testing algorithm

Rectification accounts for systematic measurement error. During rectification, measurements that are systematically in error are identified and discarded. Rectification can be done either cyclically or simultaneously with reconciliation, and either intuitively or algorithmically. Simple methods such as data validation and complicated methods using various statistical tests can be used to identify the presence of large systematic (gross) errors in the measurements. Coupled with successive elimination and addition, the measurements with the errors can be identified and discarded. No method is completely reliable. Plant-performance analysts must recognize that rectification is approximate, at best. Frequently, systematic errors go unnoticed, and some bias is likely in the adjusted measurements. 

Parameter estimation is rooted in several scientific areas with their own preferences and approaches. While linear estimation theory is a nice chapter of mathematical statistics (refs. 1-3), practical considerations are equally important in nonlinear parameter estimation. As emphasised by Bard (ref. 4), in spite of its statistical basis, nonlinear estimation is mainly a variety of computational algorithms which perform well on a class of problems but may fail on some others. In addition, most statistical tests and estimates of... 

Random numbers are defined as a sequence of numbers which lack any pattern, unlike pseudorandom numbers which starting from an arbitrary seed state, wiU tend to repeat after a certain period. In simulations, random numbers are constantly generated to model stochastic processes and other events any correlation between random numbers will have the effect of biasing the results with an unphysical correlation. In the Appendices (Sect. B.I) statistical tests were first carried out to ensure that no bias was detected in the algorithm adopted for this work. The analysis of the statistical tests showed that the random number generator was capable of producing the required level of randoumess required for this work. 

We point out that sometimes one is satisfied with lower bounds on for instance in the statistical test for localization described in Section 9.2. In this case the algorithm can be further speeded up by restricting the computation to a suitable set of random walk trajectories instead of smnming, at the step of the iteration, over y G —M — 1,...,M+1 one can sum over a subset. Our understanding of the poljmier behavior suggests that if the system size is N the endpoint of the polymer is typically at distance 0 y/N) in all regimes (and max 0),... 

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