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So I have a Likelihood function (Lk[x,y]) that is a product of 4 different gaussian functions of different combinations of parameters (x,xy,x/y and yx^4). I need to find the compatibility of my results with a reference one. I'm traying to do in the 68% of volume way:

  • Calculate the total volume integral (T) of the Likelihood in a significant region;
  • Calculate a volume (V) from the maximum point to a certain level (say height H)
  • Make the ratio V/T until it reaches ~0.68 and then check if the reference point is within the region

In order to determine what {x,y} points will be integrated (in the second step) I'm trying to use ImplicitRegion[Lk[x,y] >= H*Lk[xM,yM],{x,y}]. In other words, I want the {xi,yi} tuples such that Lk{xi,yi} are greater than a portion of the maximum (0 < H < 1). My problem apparently lies on my implementation in this ImplicitRegion. Probably I'm misunderstading something.

Thanks in advance

yohbs
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user49432
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  • I don't think that ImplicitRegion can handle such complicated conditions. Maybe a better way would be to use ContourPlot or Plot3D with MeshFunctions->{#3&} and extract the contours from the plot. If I'll have time later I'll write a solution – yohbs Jun 10 '17 at 21:22
  • See this for extracting the contours from a plot – yohbs Jun 10 '17 at 21:25

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