Random walk designs for selecting pool sizes in group testing estimation with small samples

Group testing estimation, which utilizes pooled rather than individual units for testing, has been an ongoing area of research for over six decades. While it is often argued that such methods can yield large savings in terms of resources and/or time, these benefits depend very much on the initial choice of pool sizes. In fact, when poor group sizes are used, the results can be much worse than those obtained using standard techniques. Tools for addressing this problem in the literature have been based on either large sample results or prior knowledge of the parameter being estimated, with little guidance when these assumptions are not met. In this paper, we introduce and study random walk designs for choosing pool sizes when only a small number of tests can be run and prior knowledge is vague. To illustrate these methods, application is made to the estimation of prevalence for two diseases among Australian chrysanthemum crops.