I have been working with Shannon's entropy (SE) and DNA lately, and referring to the formula and concept of SE, I just wondered whether one should in the case of DNA use each nucleotide as having a probability to show up as 0,25 or if it was better to use the probability based on the frequency in the genome (let's say the human genome).
In the case of the latter being the better, is it interesting to have those frequencies at the scale of the genome, the chromosome, the sub segment ?
I'm interested in calculating the entropy relative to a short window (the length of an Illumina read, about 125-150bases), using the proportion of each base on a given sequence length. The idea is "how much information is given" in this sequence, and by information I mean how much different bases do I have.
It might that I'm missing some basic mathematics knowledge here, don't hesitate to point it out so I can understand it better