attempted prediction model (that works in Winbugs)
Mike Conroy
At Chris's suggestion, I am posting this to the list. The problem
involves a situation where there are 2 sets of data: a calibration data
set used to predict probability of detection for different size groups
of animals in
wildlife surveys, and a second set of observed groups of different
sizes, to which the calibration predictions are applied for estimating
abundance. Chris and I have been attempting to build this model in pymc
via a variety of approaches, including the use of a potential class to
attempt to separate the issue of estimating the prediction equation from
estimating abundance. To date 1) the coefficients of the calibration
equation
wander off (e.g., predicting a negative relationship between group size
and detection) when the second (prediction) part of the model and data
are included, and 2) the results diverge greatly from a corresponding
model successfully built in Winbugs using the 'cut' function, which
isolates portions of the model that get updated with data (in my case b0
and b1 with the calibration data) from portions that are being
predicted/ imputed (the N's). See attached with extensive comments. When
this runs in Winbugs the posteriors of b0 and b1 and b0.cut and b1.cut
are identical, as they should be, and predicted size frequencies and
abundance are sensible.
I think this is basically the problem of imputing the index N for a
binomial given x and p. In the simplest case, suppose we have a
posterior distribution on p, [p|x] , from observations of x and N where
x~B(N,p). We then observe a new x* from the same population; what is
the distribution of N* associated with this x* under the model
x*~B(N*,p)? This seem like a problem that ought to be readily solvable
in Pymc, but so far we have not been able to figure out how to implement it.
thanks
Mike
--
Dr. Michael J. Conroy
Senior Research Scientist
Warnell School of Forestry and Natural Resources
University of Georgia
Athens, GA 30602 USA
Off. 3-427 Forestry Building
tel. +706-542-1167
fax +706-542-8356
Unit web page
http://coopunit.forestry.uga.edu/unit_homepage
My web page
http://coopunit.forestry.uga.edu/unit_homepage/Conroy
___________________________________________________________________________
Just published:
Conroy, M.J. and J. P. Carroll. 2009. Quantitative conservation of
vertebrates. Wiley- Blackwell. ISBN: 978-1-4051-9098-5 .
hardback: http://www.wiley.com/WileyCDA/WileyTitle/productCd-1405190981.html
paperback:
http://www.wiley.com/WileyCDA/WileyTitle/productCd-1405182288.html
Thomson, David L.; Cooch, Evan G.; Conroy, Michael J. (Eds.) .2009.
Modeling Demographic Processes in Marked Populations.
Series: Environmental and Ecological Statistics , Vol. 3. Springer.
http://www.springer.com/statistics/stats+life+sci/book/978-0-387-78150-1
_____________________________________________________________________________
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