This is a preliminary article stating and proving a new maximum entropy theorem. The entropies that we consider can be used as measures of biodiversity. In that context, the question is: for a given collection of species, which frequency distribution(s) maximize the diversity? The theorem provides the answer. The chief surprise is that although we are dealing with not just a single entropy, but...

| The problem of initial probability assignment consistent with the available information about a probabilis-tic system is called a direct problem. Jaynes' maximum en-tropy principle (MaxEnt) provides a method for solving direct problems when the available information is in the form of moment constraints. On the other hand, given a probability distribution, the problem of nding a set of constra...

The Maximum Entropy method is a practical technique for generating intensity skymaps from Compton-telescope data. The application of the method to COMPTEL data for point sources and large-scale emission is described. New developments in the method are illustrated.

We give an interpretation of the Maxi­ mum Entropy (MaxEnt) Principle in game­ theoretic terms. Based on this interpretation, we make a formal distinction between differ­ ent ways of applying Maximum Entropy dis­ tributions. MaxEnt has frequently been crit­ icized on the grounds that it leads to highly representation dependent results. Our dis­ tinction allows us to avoid this problem in many c...

Theorem 1.1 originates from the excess estimate of Abresch-Gromoll(c.f. Proposition 2.3 of [1]). The main ingredient of the proof is an application of maximum principle for subharmonic functions, and the existence of a poled function L such that ∆L ≥ 1. In our case, both maximum principle (Proposition 2.28 of [16]) and the existence of L(Lemma 2.36 of [16]) are known. For the convenience of rea...

We consider the problem of inference on one of the two parameters of a probability distribution when we have some prior information on a nuisance parameter. When a prior probability distribution on this nuisance parameter is given, the marginal distribution is the classical tool to account for it. If the prior distribution is not given, but we have partial knowledge such as a fixed number of mo...

In its modern formulation, the Maximum Entropy Principle was promoted by E.T. Jaynes, starting in the mid-fifties. The principle dictates that one should look for a distribution, consistent with available information, which maximizes the entropy. However, this principle focuses only on distributions and it appears advantageous to bring information theoretical thinking more prominently into play...

We shall find a multi-dimensional checkerboard copula of maximum entropy that matches an observed set of grade correlation coefficients. This problem is formulated as the maximization of a concave function on a convex polytope. Under mild constraint qualifications we show that a unique solution exists in the core of the feasible region. The theory of Fenchel duality is used to reformulate the p...