My offhand comment about filters and resolution is somewhat confusing even
to me. Thinking a little more precisely what you have is
P(i|x,y,e,t) - prob. of detecting a photon in bin i given (x,y,e,t)
The mapping to index space is where the instrumental characteristics enter. This function is not very practical. Instead one would integrate over a bin j to get
P(i|j) - prob. of detecting a photon in bin i given it should fall in bin j
If the indexing scheme for the bins is ordinal then this would take the form of a sparse matrix. It would only be diagonal for bins with one parameter varying.
Even this is probaby too general for a simple data model. A simpler definition, which is close to how resolution is typically described in image and spectral data, is to define "resolution" bins. It would use the same method used to describe the widths of the bins in the continuous parameter space but define a probability (say 95%) that a photon with parameter values corresponding to the center of the bin (or with any value within the bin) is counted within the resolution bin. The exact definition TBD. These resolution bins may or may not overlap.
Some more food for thought,
Frank
Received on 2003-05-12Z21:35:04