[MARMAM] New pub: A Hierarchical Bayesian model of Pollock’s Closed Robust Design and application to dolphins

Robert Rankin robertw.rankin at gmail.com
Mon Mar 21 10:16:25 PDT 2016

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
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:

Free full-text PDF:
Online R/JAGS demo at Github:
(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
- 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

* 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).

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.

    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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