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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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