Search

In the estimation of proportions by group testing, unequal sized groups results in an ambiguous ordering of the sample space, which complicates the construction of exact confidence intervals. The total number of positive groups is shown to be a suitable statistic for ordering outcomes, provided its ties are broken by the MLE. We propose an interval estimation method based on this quantity, with a mid‐P correction. Coverage is evaluated using group testing problems in plant disease assessment and virus transmission by insect vectors. The proposed method provides good coverage in a range of situations, and compares favorably with existing exact methods. [ABSTRACT FROM AUTHOR]

Site occupancy, as estimated by the probability of presence, is used for monitoring species populations. However, the detection of species at individual sites is often subject to errors. In order to accurately estimate occupancy we must simultaneously account for imperfect detectability by estimating the probability of detection. The problem with estimating occupancy arises from not knowing whether a nondetection occurred at an occupied site due to imperfect detectability (sampling zeros), or the nondetection resulting from an unoccupied site (fixed zeros). We evaluated the performance of the basic, normal approximation, studentised and percentile methods for approximating confidence limits for occupancy and detection of species. Using coverage and average interval width, we demonstrated that the studentised estimator was generally superior to the others, except when a small sample of sites are selected. Under this circumstance and when calculating limits for detection, no estimator produced reliable results. The experimental factors we considered include: (i) number of sites; (ii) number of survey occasions; (iii) probabilities of presence (occupancy) and detection; and (iv) overdispersion in the capture matrix. Similar conclusions were reached both for the simulated studies and a case study. Overall, estimation near the boundaries of the probability of occupancy and detectability was difficult. [ABSTRACT FROM AUTHOR]

Group testing has been used in many fields of study to estimate proportions. When groups are of different size, the derivation of exact confidence intervals is complicated by the lack of a unique ordering of the event space. An exact interval estimation method is described here, in which outcomes are ordered according to a likelihood ratio statistic. The method is compared with another exact method, in which outcomes are ordered by their associated MLE. Plots of theP-value against the proportion are useful in examining the properties of the methods. Coverage provided by the intervals is assessed using several realistic grouptesting procedures. The method based on the likelihood ratio, with a mid-Pcorrection, is shown to give very good coverage in terms of closeness to the nominal level, and is recommended for this type of problem. [ABSTRACT FROM AUTHOR]