Population Size Estimation Using a Few Individuals as Agents

We conduct an experiment where ten attendees of an open-air music festival are acting as Bluetooth probes. We then construct a parametric statistical model to estimate the total number of visible Bluetooth devices in the festival area. By comparing our estimate with ground truth information provided by probes at the entrances of the festival, we show that the total population can be estimated with a surprisingly low error (1.26% in our experiment), given the small number of agents compared to the area of the festival and the fact that they are regular attendees who move randomly. Also, our statistical model can easily be adapted to obtain more detailed estimates, such as the evolution of the population size over time

Population estimation with performance guarantees

Abstract — We estimate the population size by sampling uniformly from the population. Given an accuracy to which we need to estimate the population with a pre-specified confidence, we provide a simple stopping rule for the sampling process. I. SUMMARY Many applications such as species estimation [1], database sampling [2], and epidemiologic studies [3], [4], [5] call for estimating a population size based on a relatively small sample. We derive a simple, yet nearly optimal, stopping rule for sampling and an estimation formula for alphabet size from uniform samples taken from the population. We will consider an approach outlined for the species estimation problem by Good [6] further on in the summary. For a more complete survey of prior results obtained in the species estimation problem, see [1]. For problems in database sampling see [7], [2]. The results obtained in this paper are also related to capture-recapture problems [3], [4], [5], where the unknown population size is estimated given the number of samples that are recaptured (repetitions) when sampling randomly from the population. Here, we are interested in how many recaptures are necessary to estimate the population to a given accuracy with a specified confidence. Intuitively speaking, the more the number of recaptures, the better the population size can be estimated. Formally, in an n-element sample let m denote the number of distinct elements. Let r = n − m denote the number of repeated elements. For example, in c,g,c,s,g,c,v, there are n = 7 samples, there are m = 4 distinct elements, c,g,s, and v, and r = 7 − 4 = 3 repeated elements, one g and two c ′. In the following, n independent samples are drawn uniformly from a k-element population and M k n and R k n = n − M k n are the random number of distinct and repeated elements observed. We drop the subscripts and superscripts when there is no ambiguity. A. Good’s approach By linearity of expectations, E(M) = k 1