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
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!
Sabrina E. Russo
Conservation and Community Ecology Group
Department of Plant Sciences
University of Cambridge
Cambridge CB2 3EA
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