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...</equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

Objective priors, especially reference priors, have been studied extensively for spatial data in the last decade. In this paper, we study objective priors for a CAR model. In particular, the properties of the reference prior and the corresponding posterior are studied. Furthermore, we show that...