Hello, suppose one is forming a probability p(x,y), where the x,y axes are somewhat accidental and rotation is possible.
I'm thinking about whether the discrete entropy H(x,y) should change if the probability is rotated in the x,y plane. My current conclusion is that it _does_ change, at least if the entropy is estimated via bins. As a simple example, suppose the probability mass is concentrated in a single bin (that is not close to the center of rotation), but it is not a true delta function, merely concentrated. After rotation, the probability mass will often be spread into two bins, simply because it does not exactly align into one bin. This clearly changes the estimated entropy. My question: should one regard this as an artifact of the binning, or is it correct to consider that the entropy changes? ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
