Answering Two Biological Questions with a Latent Class Model via MCMC Applied to Capture-Recapture Data

A well-known method for estimating the size, N, of a certain population is the capture-recapture method (for a review see Yip et al., 1995a and Schwarz and Seber, 1999). The first motivations to the development of these methods arose in biology where researchers were interested in estimating the number of animals of a certain species (see, for instance, Schnabel, 1938, and Darroch, 1958). Subsequently, this methodology was also applied in medical and social contexts where it is important to estimate the number of subjects with a certain disease or in a particular situation (Yip et al., 1995b).

[1]  N. Ebrahimi,et al.  Bayesian capture-recapture methods for error detection and estimation of population size: Heterogeneity and dependence , 2001 .

[2]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[3]  F Bartolucci,et al.  Analysis of Capture‐Recapture Data with a Rasch‐Type Model Allowing for Conditional Dependence and Multidimensionality , 2001, Biometrics.

[4]  S. Brooks,et al.  On the Bayesian analysis of population size , 2001 .

[5]  Luca Tardella,et al.  A new Bayesian method for nonparametric capture‐recapture models in presence of heterogeneity , 2002 .

[6]  A. D. Gordon,et al.  Component and Correspondence Analysis: Dimension Reduction by Functional Approximation. , 1989 .

[7]  J. Darroch.  THE MULTIPLE-RECAPTURE CENSUS I. ESTIMATION OF A CLOSED POPULATION , 1958 .

[8]  F Merletti,et al.  National Diabetes Programs: Application of capture-recapture to count diabetes? , 1994, Diabetes Care.

[9]  E. George.  Capture—recapture estimation via Gibbs sampling , 1992 .

[10]  S. Fienberg,et al.  Classical multilevel and Bayesian approaches to population size estimation using multiple lists , 1999 .

[11]  Zoe Emily Schnabel.  The Estimation of the Total Fish Population of a Lake , 1938 .

[12]  B. J. Castledine.  A Bayesian analysis of multiple-recapture sampling for a closed population , 1981 .

[13]  Cormack Rm,et al.  Interval estimation for mark-recapture studies of closed populations. , 1992 .

[14]  A. Agresti.  Simple capture-recapture models permitting unequal catchability and variable sampling effort. , 1994, Biometrics.

[15]  Philip J. Smith.  Bayesian analyses for a multiple capture-recapture model , 1991 .

[16]  Lalitha Sanathanan,et al.  ESTIMATING THE SIZE OF A MULTINOMIAL POPULATION , 1972 .

[17]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[18]  S E Fienberg,et al.  A three-sample multiple-recapture approach to census population estimation with heterogeneous catchability. , 1993, Journal of the American Statistical Association.

[19]  L. Tierney.  A note on Metropolis-Hastings kernels for general state spaces , 1998 .

[20]  Ronald E. LaPorte,et al.  Capture-recapture and multiple-record systems estimation II: Applications in human diseases. International Working Group for Disease Monitoring and Forecasting. , 1995, American journal of epidemiology.

[21]  J. York,et al.  Bayesian methods for estimation of the size of a closed population , 1997 .

[22]  P. Green,et al.  Delayed rejection in reversible jump Metropolis–Hastings , 2001 .

[23]  L Tierney,et al.  Some adaptive monte carlo methods for Bayesian inference. , 1999, Statistics in medicine.

[24]  Ronald E. LaPorte,et al.  Capture-recapture and multiple-record systems estimation I: History and theoretical development ( Review ) , 1995 .

[25]  A. Sokal.  Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms , 1997 .

[26]  S. Fienberg.  The multiple recapture census for closed populations and incomplete 2k contingency tables , 1972 .

[27]  G. Seber,et al.  Estimating Animal Abundance: Review III , 1999 .

[28]  P. Peskun,et al.  Optimum Monte-Carlo sampling using Markov chains , 1973 .

[29]  B. Lindsay,et al.  Semiparametric Estimation in the Rasch Model and Related Exponential Response Models, Including a Simple Latent Class Model for Item Analysis , 1991 .