**Research interests**

Pi
problem and Maximum Probability (MaxProb)
method.

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.

Phi
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.

Applications:
spam filtering, recurrence
quantification analysis

list of selected works ¤ MaxProb site ¤ George Judge ¤ Robert K. Niven ¤ Arthur Ramer ¤ Laura Schechter ¤ Vladimír Špitalský ¤ iškolában

**Affiliations**

Dept. of Mathematics

Faculty of Natural Sciences

Matej Bel University

SK-974 01 Banska Bystrica

Slovakia

e-mail: marian.grendar@savba.sk

Institute of Mathematics and Computer Science

(of Mathematical Institute of Slovak Academy of Sciences (SAS) )

Severna 5

SK-974 00 Banska Bystrica

Slovakia

Institute of Measurement Science of SAS

Dubravska cesta 9

SK-841 04 Bratislava

Slovakia