We are pleased to announce our new publication on Shark Bay bottlenose dolphins which benchmarks model-averaging in Program MARK and a Bayesian Hierarchical model for temporary-migration Robust Design mark-recapture models. Rankin RW, Nicholson KE, Allen SJ, Krützen M, Bejder L, Pollock KH. 2016. A full-capture Hierarchical Bayesian model of Pollock’s Closed Robust Design and application to dolphins. Frontiers in Marine Science, 3(25). doi: 10.3389/fmars.2016.00025 URL: http://journal.frontiersin.org/article/10.3389/fmars.2016.00025
Free full-text PDF: http://researchrepository.murdoch.edu.au/30267/1/full-capture%20Hierarchical%20Bayesian%20model.pdf Online R/JAGS demo at Github: https://github.com/faraway1nspace/PCRD_JAGS_demo (plus bottlenose dolphin photo-ID data) * Alternative to AIC Model-Averaging The paper will be of interest to cetacean researchers who use Program MARK for temporary-migration Robust Design models. In particular that we show that a Hierarchical Bayesian model can yield similar estimates as model-averaging by AICc, the latter being the current best-practise to deal with the vast number of 'fixed-effects' models that one typically considers. Model-averaging and Bayesian frameworks have some similar philosophical underpinnings, such as conditioning on the data (Burnham and Anderson 2014). However, the HB framework is also highly extensible and can deal with other challenges where the AIC is undefined, such as random-effects and individual-level heterogeneity in capture-probabilities. * Mark-Recapture and low-sample sizes: the Bayesian Answer Bayesian models are a solid answer to a perennial dilemma among cetacean researchers: photo-ID datasets are typically sparse or have low-sample sizes. In contrast, researchers typically want complex data-hungry model to increase ecological realism. For example, a simple temporary-migration model or individual heterogeneity model will demand >30 - 70 variables for a mid-sized dataset. Frequentist and AICc-based inference will be overly-confident in such situations, and yield ridiculous estimates such as 100% detection, or 0% migration, or 100% survival, or just fail altogether. Alternatively, Hierarchical Bayesian models provide exact inference under low-sample sizes: they just depend more on the prior distributions, which, if set-up thoughtfully, are more conservative, make better predictions, and can automatically safeguard against over-parametrization (Berger 2006, Gelman 2013). * Individual Heterogeneity Individual heterogeneity in capture probabilities will result in biased-low population abundance estimates (see an online animation to demonstration the effect: http://mucru.org/new-pub-hierarchical-bayesian-pcrd/ ), and therefore it is a primary preoccupation of most capture-recapture practitioners. Under a Hierarchical Bayesian full-capture framework, it is trivial to model individuals as coming from a distribution, without a large increase in complexity. In contrast, the comparable fixed-effect version in Program MARK, the 'two-point finite mixture model', typically yields over-parametrized models and unreliable capture-estimates (e.g., p=1). * R and JAGS code See our online R/JAGS tutorial at Github https://github.com/faraway1nspace/PCRD_JAGS_demo for code to run the Hierarchical Bayesian Pollock's Closed Robust Design. The tutorial includes an example photo-ID bottlenose dolphin dataset from Krista et al. 2012 ( http://dx.doi.org/10.1071/MF12210). We use the flexible BUGS-like Bayesian syntax called "JAGS", which makes Bayesian models accessible to almost anyone with rudimentary scripting skills. * Key Findings - full-capture, non-hierarchical Bayesian PCRD models had slightly better estimation performance than equivalent fixed-effects Maximum-Likelihood estimation (in MARK), mainly due to the latter's susceptibility to singularities (although there was no clear champion); - we propose a Hierarchical Bayesian PCRD which can lead to similar estimates as AICc model-averaging and serve as a type of multi-model inference; - we showed how heterogeneity in detection probabilities can lead to a 8-24% increase in bottlenose dolphin abundance estimates, as compared to ML and Bayesian models that assume homogeneous detection probabilities; - we explored the partial non-identifiability and high correlation among parameter estimates, especially between survival and temporary-migration which has serious consequences for ones' ability to use these parameters for inference, and which should influence researchers' study design and modelling strategies; - we proposed two posterior predictive checks to help diagnose poor model fitting, in lieu of a formal goodness-of-fit procedure in popular CMR software. * the Bayesian Bias Some Mark users who are new to Bayesian inference may worry about prior information and the inherent bias of subjective Bayesian models. But, there is strong evidence from the machine-learning and predictive analytics community that slightly conservatively biased models yield better predictions, especially in the face of low-sample sizes and very complex models (Murphy KP, 2012). In the Learning community, this is called "Regularization", such as the Lasso or Ridge Regression or Boosting: these techniques impose a penalty on model complexity and favour simpler models than "objective" ML models estimate. Interestedly, many of the Learning communities' regularization techniques can be interpreted as Bayesian models with special priors (Hooten and Hobbs 2015). * ABSTRACT We present a Hierarchical Bayesian version of Pollock's Closed Robust Design for studying the survival, temporary-migration, and abundance of marked animals. Through simulations and analyses of a bottlenose dolphin photo-identification dataset, we compare several estimation frameworks, including Maximum Likelihood estimation (ML), model-averaging by AICc, as well as Bayesian and Hierarchical Bayesian (HB) procedures. Our results demonstrate a number of advantages of the Bayesian framework over other popular methods. First, for simple fixed-effect models, we show the near-equivalence of Bayesian and ML point-estimates and confidence/credibility intervals. Second, we demonstrate how there is an inherent correlation among temporary-migration and survival parameter estimates in the PCRD, and while this can lead to serious convergence issues and singularities among MLEs, we show that the Bayesian estimates were more reliable. Third, we demonstrate that a Hierarchical Bayesian model with carefully thought-out hyperpriors, can lead to similar parameter estimates and conclusions as multi-model inference by AICc model-averaging. This latter point is especially interesting for mark-recapture practitioners, for whom model-uncertainty and multi-model inference have become a major preoccupation. Lastly, we extend the Hierarchical Bayesian PCRD to include full-capture histories (i.e., by modelling a recruitment process) and individual-level heterogeneity in detection probabilities, which can have important consequences for the range of phenomena studied by the PCRD, as well as lead to large differences in abundance estimates. For example, we estimate 8%-24% more bottlenose dolphins in the western gulf of Shark Bay than previously estimated by ML and AICc-based model-averaging. Other important extensions are discussed. Our Bayesian PCRD models are written in the BUGS-like JAGS language for easy dissemination and customization by the community of capture-mark-recapture practitioners. Copy the following Bibtex into your favourite Reference Manager. @article{rankin_full-capture_2016, title = {A full-capture {Hierarchical} {Bayesian} model of {Pollock}'s {Closed} {Robust} {Design} and application to dolphins}, volume = {3}, url = {http://journal.frontiersin.org/article/10.3389/fmars.2016.00025}, doi = {10.3389/fmars.2016.00025}, number = {25}, journal = {Frontiers in Marine Science}, author = {Rankin, Robert W. and Nicholson, Krista E. and Allen, Simon J. and Krützen, Michael and Bejder, Lars and Pollock, Kenneth H.}, year = {2016} } "You could give Aristotle a tutorial. And you could thrill him to the core of his being ... Such is the privilege of living after Newton, Darwin, Einstein, Planck, Watson, Crick and their colleagues." -- Richard Dawkins
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