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Biometrika 2001 88(2):317-336; doi:10.1093/biomet/88.2.317
© 2001 by Biometrika Trust
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On the Bayesian analysis of population size

R.King1 and S.P. Brooks2

1 School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, U.Kruth.king{at}bris.ac.uk 2 Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, U.K.s.p.brooks{at}statslab.cam.ac.uk

We consider the problem of estimating the total size of a population from a series of incomplete census data.We observe that inference is typically highly sensitive to the choice of model and we demonstrate how Bayesian model averaging techniques easily overcome this problem. We combine and extend the work of Madigan & York (1997) and Dellaportas & Forster (1999) using reversible jump Markov chain Monte Carlo simulation to calculate posterior model probabilities which can then be used to estimate model-averaged statistics of interest. We provide a detailed description of the simulation procedures involved and consider a wide variety of modelling issues, such as the range of models considered, their parameterisation, both prior choice and sensitivity, and computational efficiency. We consider a detailed example concerning adolescent injuries in Pennsylvania on the basis of medical, school and survey data. In the context of this example, we discuss the relationship between posterior model probabilities and the associated information criteria values for model selection. We also discuss cost-efficiency issues with particular reference to inclusion and exclusion of sources on the grounds of cost. We consider a decision-theoretic approach, which balances the cost and accuracy of different combinations of data sources to guide future decisions on data collection.

Key Words: Census data; Contingency table; Cost-effectiveness; Decision theory; Log-linear model; Markov chain Monte Carlo; Posterior model probability; Reversible jump

Received March 2000. Revised December 2000


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