       BinCounts to InterpolatingFunction

• To: mathgroup at smc.vnet.net
• Subject: [mg109442] BinCounts to InterpolatingFunction
• From: "Kevin J. McCann" <Kevin.McCann at umbc.edu>
• Date: Tue, 27 Apr 2010 04:07:05 -0400 (EDT)

I am using a Markov Chain Monte Carlo (MCMC) approach to evaluate a
multidimensional probability density function. The output is a large
number of multidimensional points {x1,x2,...,xn}. I can use BinCounts to
gather the points into a PDF (after appropriate normalization). I would
like to then define a function, p[X_], which is the multidimensional
interpolation of the BinCounts output, but I can't figure out how to
automate this for an arbitrary number of dimensions.

Any ideas?

For the 2d case I did the following:

tbl = Partition[
Flatten[Table[{xmin + i*\[CapitalDelta]x + \[CapitalDelta]x/2,
ymin + j*\[CapitalDelta]y + \[CapitalDelta]y/2,
counts[[i + 1,
j + 1]]/(\[ScriptCapitalN] \[CapitalDelta]x \
\[CapitalDelta]y)}, {i, 0, nx - 1}, {j, 0, ny - 1}]], 3];

f=Interpolation[tbl]

But as you can see, this is not easily extended to higher dimensions.

Kevin

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