Via Tom LaGatta, Boris Glebov writes:
My labmates have statistics problem. We are all experimentalists, but need an input on a fine statistics point.
The problem is as follows. The data set consists of photon counts measured at a series of coordinates. The number of input photons is known, but the system transmission (T) is not known and needs to be estimated. The number of transmitted photons at each coordinate follows a binomial distribution, not a Gaussian one.
The spatial distribution of T values it then fit using a Levenberg-Marquart method modified to use weights for each data point.
At present, my labmates are not sure how to properly calculate and use the weights. The equations are designed for Gaussian distributions, not binomial ones, and this is a problem because in many cases the photon counts are near the edge (say, zero), where a Gaussian width is nonsensical.
Could you recommend a source they could use to guide their calculations?
I don’t know anything about this (although I assume I could figure out a good answer easily enough if I knew more about the model). I just thought this was worth sharing, partly because maybe some readers have a good answer and partly as an example of the wide variety of terminology used in different statistical applications.
My general advice in this sort of problem is to forget about the weights as weights and instead think about where they came from, and include in the model (typically in a likelihood function or a poststratification summary) the information that went into the weights.