Hidden Markov Models for Extended Batch Data

Cowen, Laura L. E. and Besbeas, Panagiotis and Morgan, Byron J. T. and Schwarz, Carl J. (2017) Hidden Markov Models for Extended Batch Data. Biometrics, . ISSN 0006-341X. (In press) (doi:https://doi.org/10.1111/biom.12701) (Full text available)

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http://dx.doi.org/10.1111/biom.12701

Abstract

Batch marking provides an important and efficient way to estimate the survival probabilities and population sizes of wild animals. It is particularly useful when dealing with animals that are difficult to mark individually. For the first time, we provide the likelihood for extended batch-marking experiments. It is often the case that samples contain individuals that remain unmarked, due to time and other constraints, and this information has not previously been analyzed. We provide ways of modeling such information, including an open N-mixture approach. We demonstrate that models for both marked and unmarked individuals are hidden Markov models; this provides a unified approach, and is the key to developing methods for fast likelihood computation and maximization. Likelihoods for marked and unmarked individuals can easily be combined using integrated population modeling. This allows the simultaneous estimation of population size and immigration, in addition to survival, as well as efficient estimation of standard errors and methods of model selection and evaluation, using standard likelihood techniques. Alternative methods for estimating population size are presented and compared. An illustration is provided by a weather-loach data set, previously analyzed by means of a complex procedure of constructing a pseudo likelihood, the formation of estimating equations, the use of sandwich estimates of variance, and piecemeal estimation of population size. Simulation provides general validation of the hidden Markov model methods developed and demonstrates their excellent performance and efficiency. This is especially notable due to the large numbers of hidden states that may be typically required

Item Type: Article
Uncontrolled keywords: Batch marking; Integrated population modeling; Mark-recapture; Open N-mixture models; Viterbi algorithm; Weather-loach.
Subjects: Q Science > QA Mathematics (inc Computing science)
Q Science > QL Zoology
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Byron Morgan
Date Deposited: 11 May 2017 11:27 UTC
Last Modified: 12 May 2017 09:12 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/61695 (The current URI for this page, for reference purposes)
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