Extending the Latent Multinomial Model with Complex Error Processes and Dynamic Markov Bases

Authors

Simon J. Bonner, University of Western Ontario, Canada
Matthew R. Schofield, University of Otago, New Zealand
Patrik Noren, North Carolina State University
Steven J. Price, University of KentuckyFollow

Abstract

The latent multinomial model (LMM) of Link et al. [Biometrics 66 (2010) 178–185] provides a framework for modelling mark-recapture data with potential identification errors. Key is a Markov chain Monte Carlo (MCMC) scheme for sampling configurations of the latent counts of the true capture histories that could have generated the observed data. Assuming a linear map between the observed and latent counts, the MCMC algorithm uses vectors from a basis of the kernel to move between configurations of the latent data. Schofield and Bonner [Biometrics 71 (2015) 1070–1080] shows that this is sufficient for some models within the framework but that a larger set called a Markov basis is required when errors are more complex. We address two further challenges: (1) that models with complex error mechanisms may not fit within the LMM framework and (2) that Markov bases can be difficult to compute for studies of even moderate size. We extend the framework to model the capture/demographic and error processes separately and develop a new MCMC algorithm using dynamic Markov bases. Our work is motivated by a study of queen snakes (Regina septemvittata) and we use simulation to compare estimates of survival rates when snakes are marked with PIT tags which have perfect identification versus brands which are prone to error.

Document Type

Article

Publication Date

2016

Notes/Citation Information

Published in The Annals of Applied Statistics, v. 10, no. 1, p. 246-263.

© Institute of Mathematical Statistics, 2016

The copyright holder has granted the permission for posting the article here.

Digital Object Identifier (DOI)

https://doi.org/10.1214/15-AOAS889

Related Content

Supplement to “Extending the latent multinomial model with complex error processes and dynamic Markov bases” (DOI: 10.1214/15-AOAS889SUPP). Supplement A: Proof of convergence. Proof that the chains generated by Algorithm 2 converge to the correct distribution. Supplement B: Model M_tα. Application of the extended framework with dynamic Markov bases to model M_tα.

Repository Citation

Bonner, Simon J.; Schofield, Matthew R.; Noren, Patrik; and Price, Steven J., "Extending the Latent Multinomial Model with Complex Error Processes and Dynamic Markov Bases" (2016). Forestry and Natural Resources Faculty Publications. 18.
https://uknowledge.uky.edu/forestry_facpub/18