Computer-intensive methods for uncertainty estimation in complex situations

International regulations require the specification of an uncertainty estimate related to experimental data. In chemistry, the situation that a straightforward statistical machinery is not available for assessing the uncertainty of a datum extracted from complex systems often occurs. Non-linearity, non-normality, correlation and other nuisance factors add to the complications. Monte Carlo resampling algorithms, in combination with abundant fast computing power, have made techniques feasible that do not require profound mathematical insight, but, nevertheless, are fairly general. Assessment of confidence limits at different levels of correctness is discussed using standard and bootstrap methods. Inferiority of standard normal approaches becomes evident even in mildly non-linear situations.