Supplement 1. WinBUGS model specification for the lizard example in the paper.
J. Andrew Royle
Kevin V. Young
10.6084/m9.figshare.3529757.v1
https://wiley.figshare.com/articles/Supplement_1_WinBUGS_model_specification_for_the_lizard_example_in_the_paper_/3529757
<h2>File List</h2><blockquote>
<p><a href="lizard.txt">lizard.txt</a> -- WinBUGS model specification </p>
</blockquote><h2>Description</h2><blockquote>
<p>The file lizard.txt contains the WinBUGS model specification of the spatial capture-recapture
model for the lizard data analyzed in the paper.
The coordinates of each individual's center
of activity are given by the variables
s1[i]and s2[i] which are assumed to be uniformly distributed over a box bounded by
coordinates (Xl, Xu) (easting) and (Yl, Yu) (northing).
These bounds are specified as inputs (i.e., data) to WinBUGS.
The location of each individual at each sampling occasion are specified
by the coordinate matrices U1 (easting) and U2 (northing)
which are of dimension nind + nzeroes (size of augmented data list) × T (number of samples).
The indicator variables flag1, flag2, flag3,
and flag4 keep track of where each individual is at time <i>t</i> relative to the
boundaries of the sample unit. Thus, inplot[i] is an indicator of whether
individual <i>i</i>'s activity center is within the sample unit. <br>
<br>
The WinBUGS implementation of the model is
based on data augmentation (Royle et al. 2007)
in which a large number of
all-zero encounter histories
are added to the observed data
(in the WinBUGS specification, this is
the quantity nzeroes).
Data augmentation induces a collection of latent indicator variables, z[i],
indicating whether an individual in the
augmented list is a member of the sampled population of size <i>N</i>.
Data augmentation implies the model z[i] ~ dbern(psi) and psi ~ dunif(0,1).
Together, these priors imply
that <i>N</i> is discrete uniform on the integers 0-M where M = nind + nzeroes. <br>
<br>
The following variables in the
model specification are data that must be supplied by the user:
</p>
<ul>
<li> Xl, Xu, Yl, Yu</li>
:
define the edges of a square that contains the sample plot. This box defines the region over
which individuals in the super-population of size <i>M</i> are distributed uniformly. It forms, essentially, a prior distribution for the activity centers.
<li> delta</li>
:
this is the size (width) of the buffer -- the difference between the sample plot edge and the bounding box
(for a square plot and larger square bounding box).
<li>nind</li>
:
number of individuals encountered
<li> nzeroes</li>
:
number of all-zero encounter histories added to the data set
<li> T</li>
:
number of samples (surveys, replicates)
<li> Y</li>
:
the 2-dimensional array of encounter histories including the augmented all-zero encounter
histories.
<li> U1</li>
:
the 2-dimensional matrix of easting coordinates of each individual. Non-captures are coded as missing values.
This matrix includes the augmented all-zero encounter histories, coded as missing values.
<li> U2:
the 2-dimensional matrix of northing coordinates of each individual. Non-captures are coded as missing values.
This matrix includes the augmented all-zero encounter histories, coded as missing values. </li>
</ul>
<p>The interested reader can consult the WinBUGS manual for formatting data for
input into WinBUGS. The authors used the R library R2WinBUGS. <br>
<br>
LITERATURE CITED </p>
<p>Royle, J. A., R. M. Dorazio, and W. A. Link. 2007.
Analysis of multinomial models with unknown index using data augmentation.
Journal of Computational and Graphical Statistics
16:67–85.</p>
</blockquote>
2016-08-05 08:33:40
spatial point process
data augmentation
density estimation
trapping grid
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abundance estimation
trapping web
Phrynosoma mcallii
distance sampling
hierarchical modeling
animal movement models