problem and Maximum Probability (MaxProb)
Relative Entropy Maximization (REM/MaxEnt) as an asymptotic instance of MaxProb.
Probabilistic justification of MaxProb and REM/MaxEnt via the Conditional Law of Large Numbers.
Parametric and empirical extensions of REM/MaxEnt.
problem and Bayesian
Maximum Probability (MAP) method.
Maximum Non-parametric Likelihood (MNPL) as an asymptotic instance of MAP.
Probabilistic justification of MAP and MNPL via the Bayesian Law of Large Numbers.
Large-deviations approach to the Bayesian non-parametric consistency.
Estimating Equations and Empirical Likelihood.
A brief survey of the Pi and Phi problems can be found here.
Statistical evidence: likelihood
Misc: Jeffreys entropy maximization, Golan, Judge & Miller's Generalized MaxEnt, Maximum Entropy Production, Graph entropy.
spam filtering, recurrence