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This is actually a variant of a well-known problem of how the parameters of a multinomial distribution can be estimated by maximum likelihood, and this arises from a final year project I undertook ...

I have a question related to self-calibration in radio interferometry, but I will try to phrase it as generic as possible. I have a set of data points, $D = \{ d_{0, t_0}, d_{1, t_0}, ..., d_{M, t_0}, ...