Efficient sequential Monte Carlo algorithms for integrated population models

In statistical ecology, state-space models are commonly used to represent the biological mechanisms by which population counts—often subdivided according to characteristics such as age group, gender or breeding status—evolve over time. As the counts are only noisily or partially observed, they are typically not sufficiently informative about demographic parameters of interest and must be combined with additional ecological observations within an integrated data analysis. Fitting integrated models can be challenging, especially if the constituent state-space model is nonlinear/non-Gaussian. We first propose an efficient particle Markov chain Monte Carlo algorithm to estimate demographic parameters without a need for linear or Gaussian approximations. We then incorporate this algorithm into a sequential Monte Carlo sampler to perform model comparison. We also exploit the integrated model structure to enhance the efficiency of both algorithms. The methods are demonstrated on two real data sets: little owls and grey herons. For the owls, we find that the data do not support an ecological hypothesis found in the literature. For the herons, our methodology highlights the limitations of existing models which we address through a novel regime-switching model. Supplementary materials accompanying this paper appear online.</div

Appendix B. Markov chain Monte Carlo algorithm.

Markov chain Monte Carlo algorithm

Appendix A. Prior specifications, prior sensitivity, and goodness of fit for the harbor seal example.

Prior specifications, prior sensitivity, and goodness of fit for the harbor seal example

Supplement 1. Source code and example data for implementing the Markov chain Monte Carlo algorithm.

<h2>File List</h2><div> <p><a href="MCMCalgorithm.r">MCMCalgorithm.r</a> -- (md5: 66b96318b9d549b5abd7a98178ccc6c8)</p> <p><a href="MCMCalgorithm.c">MCMCalgorithm.c</a> -- (md5: c637bb779c8f04eaf247974a6409ef1b)</p> <p><a href="MCMCalgorithm.dll">MCMCalgorithm.dll</a> -- (md5: 479e438af5b72bb05d8a413b487f8d2e)</p> <p><a href="data.RData">data.RData</a> -- (md5: 25eccac47d5082a651ec6d1040daf939)</p> <p><a href="Initial_values.RData">Initial_values.RData</a> -- (md5: 8da04b2b834f00fe2f7d8669d34e7550)</p> </div><h2>Description</h2><div> <p>MCMCalgorithm.r contains R code for loading the data (data.RData and Initial_values.RData), data pre- and post-processing, loading the dynamic link library file (MCMCalgorithm.dll), and calling the .C function for interfacing the compiled C code (MCMCalgorithm.c) with R (on a machine running Windows). </p> <p>MCMCalgorithm.c contains C code for implementing the MCMC algorithm.</p> <p>MCMCalgorithm.dll is a dynamic link library file containing the compiled C code.</p> <p>data.RData contains the data for 17 harbor seals.</p> <p>Initial_values.RData contains starting values for initialization of the MCMC chain.</p> </div

Appendix C. Posterior summaries for the harbor seal example.

Posterior summaries for the harbor seal example

Appendix B. Description of HMM model checking via pseudo-residuals, and plots of pseudo-residuals obtained in the bison application.

Description of HMM model checking via pseudo-residuals, and plots of pseudo-residuals obtained in the bison application

Appendix C. Outline of the different types of random walks, and description of how biased random walks can be fitted in the HMM framework.

Outline of the different types of random walks, and description of how biased random walks can be fitted in the HMM framework

Supplement 1. R code for fitting the individual-specific HMMs and HSMMs, for computing the HSMM residuals, for fitting the hierarchical HSMM, and observations for one of the bison, as well as an updated more efficient version of the code.

<h2>File List</h2><div> <p>(Older version)  <a href="1_individual_specific_HMMs_and_HSMMs.r">1_individual_specific_HMMs_and_HSMMs.r</a> (md5: 480705d7fbaa10185b499a13c72dff91)</p> <p><a href="2_residuals_for_HSMMs.r">2_residuals_for_HSMMs.r</a> (md5: f49e03aedde8c09cad8325ce72b87a8b)</p> <p>(Older version)  <a href="3_hierarchical_HSMM.r">3_hierarchical_HSMM.r</a> (md5: c5e3234dcbc9a81079411c26e85892d2)</p> <p><a href="4_obs.txt">4_obs.txt</a> (md5: b5eea7bba207da7711801939d10da124)</p> <p> </p> <p><b>Revised, more efficient code. Received and published 5 February 2015:</b></p> <p><a href="1_individual_specific_HMMs_and_HSMMs_revised.r.R">1_individual_specific_HMMs_and_HSMMs_revised.r.R</a> (MD5: c4ec48927645e403ed9e3c6b7df22f9f)</p> <p><a href="3_hierarchical_HSMM_revised.r.R">3_hierarchical_HSMM_revised.r.R</a> (MD5: 5f11bc3831bd8c7a93f7560d304e6f56)</p> </div><h2>Description</h2><div> The supplements give R implementations of the methods described in the paper. The first supplement gives R code for fitting individual-specific HMMs and HSMMs. The second supplement gives R code for computing residuals for fitted HSMMs. The third supplement gives R code for fitting the hierarchical HSMM described in Section 5 of the main manuscript. The fourth supplement gives an example bivariate time series, the step lengths and turning angles for one of the bison considered in the main manuscript, that can be analyzed using the first supplement.</div

Appendix F. Model fitting results, including parameter estimates for the individual-specific models, log-likelihood and AIC values for all considered models, and plots of the fitted state dwell-time distributions in the individual-specific models.

Model fitting results, including parameter estimates for the individual-specific models, log-likelihood and AIC values for all considered models, and plots of the fitted state dwell-time distributions in the individual-specific models

Appendix E. Plots of the bison movement paths.

Plots of the bison movement paths