Premium
Optimal PPS Sampling with Vanishing Auxiliary Variables – with Applications in Microscopy
Author(s) -
Andersen Ina Trolle,
Hahn Ute,
Vedel Jensen Eva B.
Publication year - 2015
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12156
Subject(s) - mathematics , sampling (signal processing) , robustness (evolution) , poisson sampling , sampling design , population , stratified sampling , statistics , mathematical optimization , algorithm , importance sampling , slice sampling , computer science , monte carlo method , biochemistry , chemistry , demography , filter (signal processing) , sociology , computer vision , gene
Recently, non‐uniform sampling has been suggested in microscopy to increase efficiency. More precisely, proportional to size (PPS) sampling has been introduced, where the probability of sampling a unit in the population is proportional to the value of an auxiliary variable. In the microscopy application, the sampling units are fields of view, and the auxiliary variables are easily observed approximations to the variables of interest. Unfortunately, often some auxiliary variables vanish, that is, are zero‐valued. Consequently, part of the population is inaccessible in PPS sampling. We propose a modification of the design based on a stratification idea, for which an optimal solution can be found, using a model‐assisted approach. The new optimal design also applies to the case where ‘vanish’ refers to missing auxiliary variables and has independent interest in sampling theory. We verify robustness of the new approach by numerical results, and we use real data to illustrate the applicability.