UBC Theses and Dissertations
Measuring sample maximums : an application to water quality monitoring Casey, Donald B.
There are many situations in which the process of obtaining a sample and the process of measuring a sample are distinct. In these circumstances, it is usual that the cost of measuring or testing the samples is significant relative to the cost of sampling. In this thesis, methods are developed for estimating the maximum sample measurement from a finite set of sequential samples without explicitly testing all of the samples. In addition to the above assumptions, it is assumed that the sample measurements are highly positively autocorrelated and that it is desirable that the estimate of the maximum sample measurement be an observed value. This objective together with the stated assumptions are of particular relevance to the area of water quality monitoring. Two different approaches are developed. These are called mathematical programming methods and composite methods. The latter approach is investigated empirically. Several composite methods are proposed with primary first order compositing being examined in detail. This method was found to be superior to the traditional technique of random sampling over a wide range of performance measures. Primary first order compositing also proved very effective at detecting extreme values and provided a more efficient estimate of the population mean. When applying primary first order compositing it is shown that all composites should be of equal size and the smaller composite sizes should be preferred.
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