Dear Bugs list,
I am modelling tree growth as a function of the diameter of the tree's
trunk and want to use a mixture distribution to account for error in
diameter measurement. I have a large dataset to parameterize the growth-
diameter relationship AND a SEPARATE data set on a SUBSET of trees in
which 2 diameter measurements have been taken on the same tree within a
short time interval so that the error in tree diameter measurement can be
estimated.
Using likelihood on the SUBSET of data in an exploratory context I found
the difference between the 2 successive measurements of tree j (error_j)
to be well-approximated by:
error_j = diameter1_j - diameter2_j
error_j ~ p*Norm(0, sigma*diameter1_j^(1/2) ) + (1-p)*Unif(Low, Upp)
where p, sigma, Low, and Upp are estimated parameters, and diameter1_j and
diameter2_j are data from the SUBSET. The uniform accounts for rare,
large errors, and the Normal accounts for routine, small errors in
measurement; all errors can be positive or negative.
I would like to use this mixture as my prior on error2_i (below) in the
growth-diameter model fit using the large data set (that lacks repeat
measurements), which contains the following expression for tree i:
Obsdiameter_i = Truediameter_i + error2_i
Where Obsdiameter_i is the measured (observed) tree diameter for tree i
and error2_i is a tree-specific error parameter and Truediameter_i is
the "true" diameter of the tree that will be used in the growth-diameter
model. I do not know from what component of the mixture distribution any
particular error2_i arises, so I don't believe the Help section on Nested
Indexing and Mixtures is relevant for me (?).
I am not sure how to parameterize such a mixture in WinBugs and cannot
seem to find analogous examples.
If I include the mixture as written above, the model is not syntactically
correct and says "unknown type of probability density." I also do not
know whether with such a mixture as a prior, my posterior distribution
will be proper.
Any advice or example Winbugs code would be greatly appreciated!
Sincerely,
Sabrina
____________________________________________________
Sabrina E. Russo
Postdoctoral Fellow
Conservation and Community Ecology Group
Department of Plant Sciences
University of Cambridge
Downing Street
Cambridge CB2 3EA
United Kingdom
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