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PoCA 3D Gaussian distribution should be tilted given the incoming and outgoing tracks #140

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GilesStrong opened this issue Oct 10, 2022 · 1 comment
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enhancement New feature or request good first issue Good for newcomers help wanted Extra attention is needed Inference Issue affects the quality of inference low priority Should be fixed eventually, but isn't urgent

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@GilesStrong
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Currently 3 uncorrelated Gaussians in x,y,z are used to model the probabilities of the PoCA being located in each of the voxels in the passive volume.
Really, thought, the PDF should account for the incoming tracks and be slightly tilted.
Potentially this could be achieved by defining a 3D Gaussian with a correlation matrix.

@GilesStrong GilesStrong added enhancement New feature or request help wanted Extra attention is needed good first issue Good for newcomers low priority Should be fixed eventually, but isn't urgent Inference Issue affects the quality of inference labels Oct 10, 2022
@GilesStrong
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Thinking about this:
Likely we'll need the use of MultiVariateNormal which lacks a CDF function, so integrating the distribution over voxels becomes non-trivial.
Potentially, rsample could be used to differentiable sample points, which then seed univariate Gaussians in XYZ of a given bandwidth, which can form a 3D KDE over volume and be integrated over voxels, but this might be expensive to compute.

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Labels
enhancement New feature or request good first issue Good for newcomers help wanted Extra attention is needed Inference Issue affects the quality of inference low priority Should be fixed eventually, but isn't urgent
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