## Abstract

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 di.usive random walks. We consider an alternative non-di.usive AR(1)-type model which appears to provide a significantly better fit to the Soay sheep data.

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 di.usive random walks. We consider an alternative non-di.usive AR(1)-type model which appears to provide a significantly better fit to the Soay sheep data.

Original language | English |
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Pages (from-to) | 1709-1732 |

Number of pages | 24 |

Journal | Annals of Applied Statistics |

Volume | 7 |

Issue number | 3 |

Early online date | 3 Oct 2013 |

DOIs | |

Publication status | Published - 2013 |

## Keywords

- Arnason-Schwarz model
- Hidden Markov model
- Markov chain
- Missing values
- Soay sheep
- State-space model
- QA Mathematics