Sanov’s Theorem and the Conditional Limit Theorem (CoLT) are established for a multicolor Pólya Eggenberger urn sampling scheme, giving the Pólya divergence and the Pólya extension to the Maximum Relative Entropy (MaxEnt) method. Pólya MaxEnt includes the standard MaxEnt as a special case. The universality of standard MaxEnt advocated by an axiomatic approach to inference for inverse problems i...

MaxEnt is one of the most widely used tools in ecology, biogeography, and evolution for modeling and mapping species distributions using presence-only occurrence records and associated environmental covariates. Despite its popularity, the exponential model implemented by MaxEnt does not directly estimate occurrence probability, the natural quantity of interest when modeling species distribution...

There are several mystifications and a couple of mysteries pertinent to MaxEnt. The mystifications, pitfalls and traps are set up mainly by an unfortunate formulation of Jaynes’ die problem, the cause célèbre of MaxEnt. After discussing the mystifications a new formulation of the problem is proposed. Then we turn to the mysteries. An answer to the recurring question ’Just what are we accomplish...

In this paper, we propose an improved principal component analysis based on maximum entropy (MaxEnt) preservation, called MaxEnt-PCA, which is derived from a Parzen window estimation of Renyi’s quadratic entropy. Instead of minimizing the reconstruction error either based on L2-norm or L1-norm, the MaxEnt-PCA attempts to preserve as much as possible the uncertainty information of the data measu...

This paper shows that: (a) given a mechanical system described by a set of independent coordinates in configuration space, (b) given an initial state of specified initial coordinates, and (c) given a situation in which the system can follow any one of a set of different possible paths with a pertinent probability pi , then the average path (defined as the weighted average positions and correspo...