Abstract
In a paper published in this journal, I addressed the following problem: under which conditions will two scientists, observing the same system and sharing the same initial information, reach the same probabilistic description upon the application of the Maximum Entropy inference principle (MaxEnt) independent of the probability distribution chosen to set up the MaxEnt procedure. This is a minimal objectivity requirement which is generally asked for scientific investigation. In the same paper, I applied the findings to a critical examination of the application of MaxEnt made in Harte’s Maximum Entropy Theory of Ecology (METE). Prof. Harte published a comment to my paper and this is my reply. For the sake of the reader who may be unaware of the content of the papers, I have tried to make this reply self-contained and to skip technical details. However, I invite the interested reader to consult the previously published papers.
Highlights
In a paper published in this journal, I addressed the following problem: under which conditions will two scientists, observing the same system and sharing the same initial information, reach the same probabilistic description upon the application of the Maximum Entropy inference principle (MaxEnt) independent of the probability distribution chosen to set up the MaxEnt procedure
I am not constructing a different theory nor am I using a different model as Harte repeatedly claims in his comment, but I am computing a different solution of exactly the same MaxEnt problem considered by Maximum Entropy Theory of Ecology (METE) using a different probability distribution
I have shown in detail that, using a different bivariate probability distribution P(n, e), the energy and abundance constraints are decoupled in the sense that they only concern the marginals of the bivariate distribution; MaxEnt prescribes, as is well known to its users, a bivariate solution which is the product of two univariate distributions
Summary
I am not constructing a different theory nor am I using a different model as Harte repeatedly claims in his comment, but I am computing a different solution of exactly the same MaxEnt problem considered by METE using a different probability distribution. In the application of MaxEnt, the choice of probability distribution and the form of the entropy. The natural question that arises is as follows: what choice of probability distribution is justified in using the entropy function in Shannon form? The bivariate distribution R(n, e) used by METE and the one P(n, e) used in [2] are related by a diffeomorphism (Equation (33) in [2]) but the entropy function adopted in METE and [2] are not related by the same diffeomorphism, they produce different solutions of the same extremization problem
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