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Estimating population size with imperfect detection using a parametric bootstrap
Author(s) -
Madsen Lisa,
Dalthorp Dan,
Huso Manuela Maria Patrizia,
Aderman Andy
Publication year - 2020
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.2603
Subject(s) - statistics , mathematics , sample size determination , parametric statistics , confidence interval , population , coverage probability , estimator , sampling (signal processing) , statistical power , nominal level , population size , computer science , demography , filter (signal processing) , sociology , computer vision
We develop a novel method of estimating population size from imperfectly detected counts of individuals and a separate estimate of detection probability. Observed counts are separated into classes within which detection probability is assumed constant. Within a detection class, counts are modeled as a single binomial observation X with success probability p where the goal is to estimate index N . We use a Horvitz–Thompson‐like estimator for N and account for uncertainty in both sample data and estimated success probability via a parametric bootstrap. Unlike capture–recapture methods, our model does not require repeated sampling of the population. Our method is able to achieve good results, even with small X . We show in a factorial simulation study that the median of the bootstrapped sample has small bias relative to N and that coverage probabilities of confidence intervals for N are near nominal under a wide array of scenarios. Our methodology begins to break down when P ( X =0)>0.1 but is still capable of obtaining reasonable confidence coverage. We illustrate the proposed technique by estimating (1) the size of a moose population in Alaska and (2) the number of bat fatalities at a wind power facility, both from samples with imperfect detection probabilities, estimated independently.