Confidence intervals for priority sampling

Abstract

With a priority sample from a set of weighted items, we can provide an unbiased estimate of the total weight of any subset. The strength of priority sampling is that it gives the best possible estimate variance on any set of input weights.For a concrete subset, however, the variance on the estimate of its weight depends strongly on the total set of weights and the distribution of the subset in this set. The variance is, for example, much smaller if weights are heavy tailed.In this paper we show how to generate a confidence interval directly from a priority sample, thus complementing the weight estimates with concrete lower and upper bounds. In particularly we will tell how heavy subsets can likely be hidden when the priority estimate for a subset is zero.Our confidence intervals for priority sampling are evaluated on real and synthetic data and compared with confidence intervals obtained with uniform sampling, weighted sampling with replacement, and threshold sampling.