Inverse sequential procedures for the monitoring of time series

Climate changes traditionally have been detected from long series of observations and long after they happened. The 'inverse sequential' monitoring procedure is designed to detect changes as soon as they occur. Frequency distribution parameters are estimated both from the most recent existing set of observations and from the same set augmented by 1,2,...j new observations. Individual-value probability products ('likelihoods') are then calculated which yield probabilities for erroneously accepting the existing parameter(s) as valid for the augmented data set and vice versa. A parameter change is signaled when these probabilities (or a more convenient and robust compound 'no change' probability) show a progressive decrease. New parameters are then estimated from the new observations alone to restart the procedure. The detailed algebra is developed and tested for Gaussian means and variances, Poisson and chi-square means, and linear or exponential trends; a comprehensive and interactive Fortran program is provided in the appendix