CHAPTER 7: MAXIMUM ENTROPY METHODS

The maximum entropy method, originating from Jaynes’ maximum entropy principle, has been a numerical scheme that recovers a density function when its several moments are known. From Shannon’s entropy for discrete sample spaces to Boltzmann’s entropy for density functions and to the invention of the spline maximum entropy method, we survey some of the historical developments of this method in the past decades for the computation of important density functions, particularly for the stationary densities of Markov operators and invariant densities of Frobenius–Perron operators.