I am fiddling with some Bayesian probabilities for some astronomical data analysis. I have a ccd image and am testing the null hypothesis (no signal is present - all contributions due to noise) on it. Each ccd pixel has contributions from:
- dark counts (scale with integration time)
- readout noise (approx 3 counts)
- scattered light (approximately Poisson distributed noise with a variable mean over the format, that I locally approximate. Mean usually 20-60 counts)
- signal (Poisson distributed, count levels anywhere from 0 to >10,000)
Assuming I know the first three, i.e. the readout noise, dark counts, and the mean/variance of the scattered light, what can I treat as my error in the observed value of a pixel? As the four are uncorrelated, can I simply sum their variances linearly?
Further, given data with some signal and the previous known quantities, what is the best way to compute a probability of the given data being generated by the noise? I have tried treating each pixel as its own uncorrelated random variable, but this does not make intuitive sense: the signal photons will be spread over several pixels due to the point spread function of the optics, so local correlation between pixels seems reasonable.