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Capture–recapture estimation by means of empirical Bayesian smoothing with an application to the geographical distribution of hidden scrapie in Great Britain

Capture–recapture estimation by means of empirical Bayesian smoothing with an application to the geographical distribution of hidden scrapie in Great Britain
Capture–recapture estimation by means of empirical Bayesian smoothing with an application to the geographical distribution of hidden scrapie in Great Britain
The paper discusses population size estimation on the basis of a frequency distribution of zero-truncated counts and is motivated by a study on the geographical distribution of hidden scrapie in Great Britain. Aggregation of scrapie cases is considered at the county level and results in sparse zero-truncated count distributions which make the application of conventional capture–recapture procedures for estimating the hidden part of the scrapie-affected population difficult. We suggest a smoothed generalization of Zelterman's estimator of population size which overcomes the overestimation bias of the conventional Zelterman estimator and instead produces a lower bound, which is typically larger than Chao's lower bound estimator. The estimator uses an empirical Bayes approach with various choices for the prior distribution including a parametric choice of the gamma distribution as well as various non-parametric distributions. A simulation study investigates the performance of the new estimators, and also in comparison with conventional estimators. The empirical Bayes estimator with a non-parametric mixture model as prior performs well and the boundary problem of the conventional non-parametric discrete mixture model estimator leading to spurious population size is avoided. In the application to hidden scrapie in Great Britain the new estimators lead to maps of scrapie of observed–hidden ratios as well as completeness of the current surveillance system
capture–recapture, empirical Bayes methods, geographical analysis, non-parametric mixture model
0035-9254
723-741
Böhning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
Kuhnert, Ronny
8518a8ac-54e5-4117-b66b-66a82fdece7c
Del Rio Vilas, Victor Javier
c439650f-6c9d-42c1-80a2-2fa570de525f
Böhning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
Kuhnert, Ronny
8518a8ac-54e5-4117-b66b-66a82fdece7c
Del Rio Vilas, Victor Javier
c439650f-6c9d-42c1-80a2-2fa570de525f

Böhning, Dankmar, Kuhnert, Ronny and Del Rio Vilas, Victor Javier (2011) Capture–recapture estimation by means of empirical Bayesian smoothing with an application to the geographical distribution of hidden scrapie in Great Britain. Journal of the Royal Statistical Society, Series C (Applied Statistics), 60 (5), 723-741. (doi:10.1111/j.1467-9876.2011.01018.x).

Record type: Article

Abstract

The paper discusses population size estimation on the basis of a frequency distribution of zero-truncated counts and is motivated by a study on the geographical distribution of hidden scrapie in Great Britain. Aggregation of scrapie cases is considered at the county level and results in sparse zero-truncated count distributions which make the application of conventional capture–recapture procedures for estimating the hidden part of the scrapie-affected population difficult. We suggest a smoothed generalization of Zelterman's estimator of population size which overcomes the overestimation bias of the conventional Zelterman estimator and instead produces a lower bound, which is typically larger than Chao's lower bound estimator. The estimator uses an empirical Bayes approach with various choices for the prior distribution including a parametric choice of the gamma distribution as well as various non-parametric distributions. A simulation study investigates the performance of the new estimators, and also in comparison with conventional estimators. The empirical Bayes estimator with a non-parametric mixture model as prior performs well and the boundary problem of the conventional non-parametric discrete mixture model estimator leading to spurious population size is avoided. In the application to hidden scrapie in Great Britain the new estimators lead to maps of scrapie of observed–hidden ratios as well as completeness of the current surveillance system

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More information

e-pub ahead of print date: 29 September 2011
Published date: November 2011
Keywords: capture–recapture, empirical Bayes methods, geographical analysis, non-parametric mixture model
Organisations: Statistics, Statistical Sciences Research Institute

Identifiers

Local EPrints ID: 210461
URI: https://eprints.soton.ac.uk/id/eprint/210461
ISSN: 0035-9254
PURE UUID: 7efbb78c-f034-470f-ae45-054915414a5a
ORCID for Dankmar Böhning: ORCID iD orcid.org/0000-0003-0638-7106

Catalogue record

Date deposited: 09 Feb 2012 11:42
Last modified: 20 Jul 2019 00:44

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