Different splitting techniques with application to air pollution models

Splitting techniques are commonly used when large-scale models, which appear in different fields of science and engineering, are treated numerically. Four types of splitting procedures are defined and discussed. The problem of the choice of a splitting procedure is investigated. Several numerical tests, by which the influence of the splitting errors on the accuracy of the results is studied, are given. It is shown that the splitting errors decrease linearly when (1) the splitting procedure is of first order and (2) the splitting errors are dominant. Three examples for splitting procedures used in all large-scale air pollution models are presented. Numerical results obtained by a particular air pollution model, Unified Danish Eulerian Model (UNI-DEM), are given and analysed.

A bagging-based correction for the mixture model estimator of population size

Estimation of a population size by means of capture-recapture techniques is an important problem occurring in many areas of life and social sciences. We consider the frequencies of frequencies situation, where a count variable is used to summarize how often a unit has been identified in the target population of interest. The distribution of this count variable is zero-truncated since zero identifications do not occur in the sample. As an application we consider the surveillance of scrapie in Great Britain. In this case study holdings with scrapie that are not identified (zero counts) do not enter the surveillance database. The count variable of interest is the number of scrapie cases per holding. For count distributions a common model is the Poisson distribution and, to adjust for potential heterogeneity, a discrete mixture of Poisson distributions is used. Mixtures of Poissons usually provide an excellent fit as will be demonstrated in the application of interest. However, as it has been recently demonstrated, mixtures also suffer under the so-called boundary problem, resulting in overestimation of population size. It is suggested here to select the mixture model on the basis of the Bayesian Information Criterion. This strategy is further refined by employing a bagging procedure leading to a series of estimates of population size. Using the median of this series, highly influential size estimates are avoided. In limited simulation studies it is shown that the procedure leads to estimates with remarkable small bias.