As part of my research, I am having to fit data, which has normal errors, with a model. Until now, I have been assuming that the model values are exact, and I have therefore been able to simply use chi-squared fitting to estimate the best fit parameters and the covariance matrix.
However, each model point actually is not exact, and has errors given by Poisson statistics. In this case, it's not clear to me what quantify we are trying to minimize/maximize in order to find the best fitting model? I am primarily concerned with the best-fitting value.
If I had to guess, I would say that I am probably trying to maximize the sum of the integral (for each point) of the product of the probability distribution of the data with that of the model? Is this correct?
Any advice welcome :-)
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