Conditional distribution pollutants, estimation

Concentration estimate and associated probability, Isopleth maps, 115f Conditional distribution approach, assessment of spatial distributions of pollutants, 112-14 Conditional distribution of... 

Ideally, to characterize the spatial distribution of pollution, one would like to know at each location x within the site the probability distribution of the unknown concentration p(x). These distributions need to be conditional to the surrounding available information in terms of density, data configuration, and data values. Most traditional estimation techniques, including ordinary kriging, do not provide such probability distributions or "likelihood of the unknown values pC c). Utilization of these likelihood functions towards assessment of the spatial distribution of pollutants is presented first then a non-parametric method for deriving these likelihood functions is proposed. 

Local variations in the vertical distribution of radionuclides are determined by both hydrological and ecological conditions. The correlation between these conditions is a function of the season. Table 6.12 gives estimates of the role of ecological processes in the formation of the vertical distribution of the radionuclear pollution of Arctic seas. These estimates show that the biological community plays a minor role in radionuclide transport from upper layers to the deep ocean. 

Frequentist methods are fundamentally predicated upon statistical inference based on the Central Limit Theorem. For example, suppose that one wishes to estimate the mean emission factor for a specific pollutant emitted from a specific source category under specific conditions. Because of the cost of collecting measurements, it is not practical to measure each and every such emission source, which would result in a census of the actual population distribution of emissions. With limited resources, one instead would prefer to randomly select a representative sample of such sources. Suppose 10 sources were selected. The mean emission rate is calculated based upon these 10 sources, and a probability distribution model could be fit to the random sample of data. If this process is repeated many times, with a different set of 10 random samples each time, the results will vary. The variation in results for estimates of a given statistic, such as the mean, based upon random sampling is quantified using a sampling distribution. From sampling distributions, confidence intervals are obtained. Thus, the commonly used 95% confidence interval for the mean is a frequentist inference... 

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