The Pólya information divergence

Extensions of Sanov’s Theorem and the Conditional Limit Theorem (CoLT) are established for a multicolor Pólya-Eggenberger (PE) urn sampling scheme, giving the Pólya information divergence and a Pólya extension to the Maximum Relative Entropy (MaxEnt) method. Pólya MaxEnt includes the standard MaxEnt, as well as its variants used in Bose–Einstein, Fermi–Dirac and intermediate (Acharya-Swamy) statistics, as special cases. In the PE setting, standard MaxEnt is, in general, asymptotically inconsistent.