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.
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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: http://eprints.soton.ac.uk/id/eprint/342535
ISSN: 1061-8600
PURE UUID: 84a5a790-7c87-400f-9cb3-04bbb2132b2b
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Date deposited: 06 Sep 2012 07:42
Last modified: 15 Mar 2024 03:39
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Contributors
Author:
M. Fazil Baksh
Author:
Rattana Lerdsuwnasri
Author:
James Gallagher
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