What is a "Hierarchical Bayes" approach?
This is a standard Bayesain trick which is used commonly in
statistical circles.
A simple example easily illustrates it.
Imagine a pumping system which has four pumps. Suppose that we have
prior information about the general class of pumps consisting of
one-half failure in 121 months of standby operation and test data for
the four individual pumps consisting of 4 failures for pump A and 2
for pump C in 240 months of standby operation. What we would like to
do is to draw inferences about the failure rates in standby operation.
We posit a model in which there is a single "average" failure rate for
all pumps and then the failure rates for the four individual pumps are
that failure rate plus an offset (actually, in this case I'd use a
multiplicative offset). We can use these data to learn posteriors for
both the class of all pumps and the offsets for the individual pumps.
We need to make some strong prior assumption about the variance of the
offsets to fit the model.
[As an asside, this is a handy method for getting around the the
global independence assumption. I had an earlier paper about this in
the graphical models conference in Seattle.]
There have been many applications of this idea over the past decade or
so (after MC^2 made it easy to fit). It is commonly used for
Meta-Analysis (synthizing the results of many studies). Also it is
often used to model cluster effects in cluster sample surveys
(e.g., students within schools, schools within states). These often
lead to multi-stage hierarchical models.
Andrew Gelmann had a nice example where he was using it to smooth data
on cancer rates. The data were given by county, but some of the
counties were so small that they only had 0 or 1 reported death from
this cancer type in a year. By using a hierarchical model he could
borrow strength from the overall cancer rate for the smaller
counties. In this "Bayesian Smoothing" technique, counties with a
small size would tend to be strongly pulled toward the state mean,
which larger counties would have a comparatively smaller change from
the data values.
I haven't looked at the article in question, so I can't answer more
specifically, but I hope this helps.
--Russell Almond
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