Open Access
September 2013 Maximum likelihood estimation of mark–recapture–recovery models in the presence of continuous covariates
Roland Langrock, Ruth King
Ann. Appl. Stat. 7(3): 1709-1732 (September 2013). DOI: 10.1214/13-AOAS644


We consider mark–recapture–recovery (MRR) data of animals where the model parameters are a function of individual time-varying continuous covariates. For such covariates, the covariate value is unobserved if the corresponding individual is unobserved, in which case the survival probability cannot be evaluated. For continuous-valued covariates, the corresponding likelihood can only be expressed in the form of an integral that is analytically intractable and, to date, no maximum likelihood approach that uses all the information in the data has been developed. Assuming a first-order Markov process for the covariate values, we accomplish this task by formulating the MRR setting in a state-space framework and considering an approximate likelihood approach which essentially discretizes the range of covariate values, reducing the integral to a summation. The likelihood can then be efficiently calculated and maximized using standard techniques for hidden Markov models. We initially assess the approach using simulated data before applying to real data relating to Soay sheep, specifying the survival probability as a function of body mass. Models that have previously been suggested for the corresponding covariate process are typically of the form of diffusive random walks. We consider an alternative nondiffusive AR(1)-type model which appears to provide a significantly better fit to the Soay sheep data.


Download Citation

Roland Langrock. Ruth King. "Maximum likelihood estimation of mark–recapture–recovery models in the presence of continuous covariates." Ann. Appl. Stat. 7 (3) 1709 - 1732, September 2013.


Published: September 2013
First available in Project Euclid: 3 October 2013

zbMATH: 06237194
MathSciNet: MR3127965
Digital Object Identifier: 10.1214/13-AOAS644

Keywords: Arnason–Schwarz model , Hidden Markov model , Markov chain , missing values , Soay sheep , state-space model

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.7 • No. 3 • September 2013
Back to Top