Dear all,
I am a little stuck with a particular problem regarding the
extrapolation of a linear trend from a set of posterior distributions.
I have a Bayesian model which I have simulated in WinBUGS to produce
posterior distributions about a vector of 19 parameters which I will
call y(1), y(2),... y(19).
I also have data pertaining to a "standard" vector of 22 parameters
which I will call x(1), x(2),... x(22).
My aim is to use a weighted least squares regression to extrapolate
beyond y(19) and thus predict y(20), y(21) and y(22) using the linear
formula:
y(i) = a + b*[x(i)]
with a and b obtained from the weighted least squares regression.
After this, I will be calculating a single final parameter, z, which is
a function of y(1),... y(22) (i.e. the entire y vector). I would like
information on the uncertainty of z to be retained.
I'm a little stumped as to how to do this. Is it possible to do this
directly in WinBUGS within the same model syntax or is it better to take
the posterior distributions derived from the first model and perform the
extrapolation (and subsequent calculation of z) using different software?
Any insights (or useful references) on this would be gratefully received
- I will post a synthesis of responses in a couple of days' time.
Many thanks,
Michael Grayer.
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Michael Grayer
ESRC/CASE PhD Student
Department of Geography
Queen Mary, University of London
London E1 4NS
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