Sparse encoding of stationary distributions in AAGTR
I have some doubts regarding the way we encode stationary distributions in AAGTR in order to work with Nelder-Mead. See the decoding function.
Currently we encode n values for a profile of n AA, compute their exponential and normalize at the end. This is correct but uses one more parameter than needed. This is not so great as it means one more element in the "swarm" used by Nelder-Mead, but above all it might make the parameter space harder to explore (because different vectors proposed by Nelder-Mead are in fact equivalent). This is a potentially impacting change to consider so it needs to be done with care tests.
What do you think @louis.duchemin?