Meaning of bin-to-bin independence of data in a binned distribution

What does it mean for data bins to be “independent” in a binned distribution (like, for instance, the time series of the number of newly identified disease cases each week)?  This means that the stochastic variation data in the i^th bin is uncorrelated to the variation in the j^th bin.   You should be aware that for epidemic data, this assumption is perhaps (probably) not satisfied, but the academic body of work related to this topic currently has not come up with a good way of assessing the bin-to-bin correlations, so for now we have little choice but to assume they are uncorrelated. Note that the assumption of independent bins underlies the Maximum Likelihood, Least Squares and Pearson chi-squared methods, unless special modification is made to those methods to take the correlations into account.


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