A tobacco field in Greece was sampled during the 2001 and 2002 growing seasons to assess the seasonal trends in densities and spatial distributions of the aphid Myzus persicae (Sulzer) and its predatory mirid Macrolophus costalis (Fieber). On repeated occasions between June (just after the transplantation) and September (just before harvest), 20 tobacco leaves (10 from the upper and 10 from the lower plant part) were taken from randomly chosen plants. These leaves were sampled for aphids and mirids. In both years, the highest aphid densities were recorded during July and August, while aphid numbers were low in September. In contrast, the majority of M. costalis individuals were found during September when aphid numbers were low. Significantly more M. persicae individuals were found in the upper part of the plants, whereas significantly more M. costalis individuals were found in the lower part of the plants. As indicated by Taylor's Power Law estimates, both species were aggregated in their spatial distributions among sampling units (leaves). Wilson and Room's model, based on the Taylor's estimates, was used to calculate the mean number of aphids and mirids, from the proportion of sampling units (leaves) that had > 0 individuals of each species. This model provided a satisfactory fit of the data for both the aphid and the mirid. In addition, Wilson and Room's model was successfully used to predict the mean number of aphids and mirids in a series of samples that were carried out in the same area between June and September 2003 for model validation. Finally, equations are given for the calculation of precision in estimating the mean number of aphids or mirids per sampling unit, and the required sample size for a given level of precision.
Former authors claimed that, due to parasites' aggregated distribution, small samples underestimate the true population mean abundance. Here we show that this claim is false or true, depending on what is meant by 'underestimate' or, mathematically speaking, how we define 'bias'. The 'how often' and 'on average' views lead to different conclusions because sample mean abundance itself exhibits an aggregated distribution: most often it falls slightly below the true population mean, while sometimes greatly exceeds it. Since the several small negative deviations are compensated by a few greater positive ones, the average of sample means approximates the true population mean., Jenő Reiczigel, Lajos Rózsa., and Obsahuje bibliografii
The paper deals with the particle filter in state estimation of a discrete-time nonlinear non-Gaussian system. The goal of the paper is to design a sample size adaptation technique to guarantee a quality of a filtering estimate produced by the particle filter which is an approximation of the true filtering estimate. The quality is given by a difference between the approximate filtering estimate and the true filtering estimate. The estimate may be a point estimate or a probability density function estimate. The proposed technique adapts the sample size to keep the difference within pre-specified bounds with a pre-specified probability. The particle filter with the proposed sample size adaptation technique is illustrated in a numerical example.