Rao-Blackwellization to give Improved Estimates in Multi-List Studies

TL;DR

This paper develops Rao-Blackwellization techniques for closed population mark-recapture models, improving estimators by leveraging sufficient statistics and MCMC methods, with simulation evidence showing significant enhancements.

Contribution

It introduces Rao-Blackwellization for estimators not directly functions of sufficient statistics in mark-recapture models, including MCMC resampling procedures.

Findings

Significant estimator improvements demonstrated through simulations

Rao-Blackwellization effectively reduces estimator variance

MCMC methods enable practical computation of complex estimators

Abstract

Sufficient statistics are derived for the population size and parameters of commonly used closed population mark-recapture models. Rao-Blackwellization details for improving estimators that are not functions of the statistics are presented. As Rao-Blackwellization entails enumerating all sample reorderings consistent with the sufficient statistic, Markov chain Monte Carlo resampling procedures are provided to approximate the computationally intensive estimators. Simulation studies demonstrate that significant improvements can be made with the strategy. Supplementary materials for this article are available online.