Partial identification and dependence-robust confidence intervals for capture-recapture surveys

by   Jinghao Sun, et al.

Capture-recapture (CRC) surveys are widely used to estimate the size of a population whose members cannot be enumerated directly. When k capture samples are obtained, counts of unit captures in subsets of samples are represented naturally by a 2^k contingency table in which one element – the number of individuals appearing in none of the samples – remains unobserved. In the absence of additional assumptions, the population size is not point-identified. Assumptions about independence between samples are often used to achieve point-identification. However, real-world CRC surveys often use convenience samples in which independence cannot be guaranteed, and population size estimates under independence assumptions may lack empirical credibility. In this work, we apply the theory of partial identification to show that weak assumptions or qualitative knowledge about the nature of dependence between samples can be used to characterize a non-trivial set in which the true population size lies with high probability. We construct confidence sets for the population size under bounds on pairwise capture probabilities, and bounds on the highest order interaction term in a log-linear model using two methods: test inversion bootstrap confidence intervals, and profile likelihood confidence intervals. We apply these methods to recent survey data to estimate the number of people who inject drugs in Brussels, Belgium.



There are no comments yet.


page 4


Confidence Intervals for Seroprevalence

This paper concerns the construction of confidence intervals in standard...

Estimation of population size based on capture recapture designs and evaluation of the estimation reliability

We propose a modern method to estimate population size based on capture-...

A bootstrap analysis for finite populations

Bootstrap methods are increasingly accepted as one of the common approac...

Modeling the marked presence-only data: a case study of estimating the female sex worker size in Malawi

Continued fine-scale mapping of HIV/AIDS populations is needed to meet g...

Confidence sequences for sampling without replacement

Many practical tasks involve sampling sequentially without replacement f...

Optimized Partial Identification Bounds for Regression Discontinuity Designs with Manipulation

The regression discontinuity (RD) design is one of the most popular quas...

Doubly robust capture-recapture methods for estimating population size

Estimation of population size using incomplete lists (also called the ca...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.