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I am trying to learn the mutual information matrix of single-cell qPCR data using the infotheo R package. As with many such packages, one of the parameters for mutual information is the method of entropy estimation. For example, the options in this particular package are: empirical probability distribution, Miller-Madow asymptotic corrected empirical estimator, shrinkage estimate of the Dirichlet probability distribution, Schurman-Grassberger estimate of the Dirichlet probability.

My question, which is not specific to this package, is: How does one choose an estimator when approaching such a problem? I don't understand how one would know why one choice would make more mathematical/biological sense than another.

I don't want to just use the default setting because I can't think of a reason why not to, or because it is the most commonly used method.

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