Objective Bayesian analysis for a capture–recapture model
In this paper, we study a special capture–recapture model, the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$M_t$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>M</mi> <mi>t</mi> </msub> </math> </EquationSource> </InlineEquation> model, using objective Bayesian methods. The challenge is to find a justified objective prior for an unknown population size <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$N$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>N</mi> </math> </EquationSource> </InlineEquation>. We develop an asymptotic objective prior for the discrete parameter <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$N$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>N</mi> </math> </EquationSource> </InlineEquation> and the Jeffreys’ prior for the capture probabilities <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\varvec{\theta }$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="bold-italic">θ</mi> </mrow> </math> </EquationSource> </InlineEquation>. Simulation studies are conducted and the results show that the reference prior has advantages over ad-hoc non-informative priors. In the end, two real data examples are presented. Copyright The Institute of Statistical Mathematics, Tokyo 2014
