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Subject:

mixture of Norm and Unif

From:

=?iso-8859-1?Q?Sabrina_Russo?= <[log in to unmask]>

Reply-To:

=?iso-8859-1?Q?Sabrina_Russo?= <[log in to unmask]>

Date:

Mon, 16 Oct 2006 15:09:06 +0100

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (68 lines)

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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