Use of the ratio plot in capture-recapture estimation

Use of the ratio plot in capture-recapture estimation

Statistical graphics are a fundamental, yet often overlooked, set of components in the repertoire of data analytic tools. Graphs are quick and efficient, yet simple instruments of preliminary exploration of a dataset to understand its structure and to provide insight into influential aspects of inference such as departures from assumptions and latent patterns. In this paper, we present and assess a graphical device for choosing a method for estimating population size in capture-recapture studies of closed populations. The basic concept is derived from a homogeneous Poisson distribution where the ratios of neighboring Poisson probabilities multiplied by the value of the larger neighbor count are constant. This property extends to the zero-truncated Poisson distribution which is of fundamental importance in capture–recapture studies. In practice however, this distributional property is often violated. The graphical device developed here, the ratio plot, can be used for assessing specific departures from a Poisson distribution. For example, simple contaminations of an otherwise homogeneous Poisson model can be easily detected and a robust estimator for the population size can be suggested. Several robust estimators are developed and a simulation study is provided to give some guidance on which should be used in practice. More systematic departures can also easily be detected using the ratio plot. In this paper, the focus is on Gamma-mixtures of the Poisson distribution which leads to a linear pattern (called structured heterogeneity) in the ratio plot. More generally, the paper shows that the ratio plot is monotone for arbitrary mixtures of power series densities.

chao and robust and generalized chao estimator, closed population, generalized turing estimator, ord plot, poisson-gamma model, ratio plot, robust turing estimator, structured heterogeneity, turing estimator

135-155

Boehning, Dankmar

1df635d4-e3dc-44d0-b61d-5fd11f6434e1

Baksh, M. Fazil

576d4d2d-2cb4-4d78-a892-716fc03d2088

Lerdsuwnasri, Rattana

c2e5269d-3836-49d0-8989-753e6e33dc35

Gallagher, James

4279d3ea-61c8-4fdb-8834-ad81757cd7f5

27 March 2013

Boehning, Dankmar

1df635d4-e3dc-44d0-b61d-5fd11f6434e1

Baksh, M. Fazil

576d4d2d-2cb4-4d78-a892-716fc03d2088

Lerdsuwnasri, Rattana

c2e5269d-3836-49d0-8989-753e6e33dc35

Gallagher, James

4279d3ea-61c8-4fdb-8834-ad81757cd7f5

Boehning, Dankmar, Baksh, M. Fazil, Lerdsuwnasri, Rattana and Gallagher, James
(2013)
Use of the ratio plot in capture-recapture estimation.
*Journal of Computational and Graphical Statistics*, 22 (1), .
(doi:10.1080/10618600.2011.647174).

## Abstract

Statistical graphics are a fundamental, yet often overlooked, set of components in the repertoire of data analytic tools. Graphs are quick and efficient, yet simple instruments of preliminary exploration of a dataset to understand its structure and to provide insight into influential aspects of inference such as departures from assumptions and latent patterns. In this paper, we present and assess a graphical device for choosing a method for estimating population size in capture-recapture studies of closed populations. The basic concept is derived from a homogeneous Poisson distribution where the ratios of neighboring Poisson probabilities multiplied by the value of the larger neighbor count are constant. This property extends to the zero-truncated Poisson distribution which is of fundamental importance in capture–recapture studies. In practice however, this distributional property is often violated. The graphical device developed here, the ratio plot, can be used for assessing specific departures from a Poisson distribution. For example, simple contaminations of an otherwise homogeneous Poisson model can be easily detected and a robust estimator for the population size can be suggested. Several robust estimators are developed and a simulation study is provided to give some guidance on which should be used in practice. More systematic departures can also easily be detected using the ratio plot. In this paper, the focus is on Gamma-mixtures of the Poisson distribution which leads to a linear pattern (called structured heterogeneity) in the ratio plot. More generally, the paper shows that the ratio plot is monotone for arbitrary mixtures of power series densities.

Full text not available from this repository.

## More information

e-pub ahead of print date: 27 December 2011

Published date: 27 March 2013

Keywords:
chao and robust and generalized chao estimator, closed population, generalized turing estimator, ord plot, poisson-gamma model, ratio plot, robust turing estimator, structured heterogeneity, turing estimator

Organisations:
Statistics, Statistical Sciences Research Institute, Primary Care & Population Sciences

## Identifiers

Local EPrints ID: 342535

URI: https://eprints.soton.ac.uk/id/eprint/342535

ISSN: 1061-8600

PURE UUID: 84a5a790-7c87-400f-9cb3-04bbb2132b2b

## Catalogue record

Date deposited: 06 Sep 2012 07:42

Last modified: 06 Oct 2018 00:32

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## Contributors

Author:
M. Fazil Baksh

Author:
Rattana Lerdsuwnasri

Author:
James Gallagher

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