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Maximum Entropy Methods (MaxEnt)

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The maximum entropy method is usually stated in a deceptively simple way: from among all the probability distributions compatible with empirical data, pick the one with the highest information-theoretic entropy. To really understand where this comes from, and appreciate it at its proper worth, we need to look at its origins in equilibrium statistical mechanics. We start with an assemblage of N particles; they each have a three-dimensional position and momentum, and possibly some internal degrees of freedom, so the dimension of the microscopic state space, or phase space, is at least 6N. We define some macroscopic observables; these are functions of the microscopic state, so they partition phase space into regions where the macrovariables are constant. A macroscopic state is a value for the macroscopic variables, which, in extension, corresponds to one of these regions of phase space. Boltzmann's postulate is that the probability of a macroscopic state is proportional to the volume of m

Maximum Entropy Methods (MaxEnt) Notebooks Maximum Entropy Methods (MaxEnt) Last update : 07 Jul 2025 12:23 First version : 27 August 2006; major expansion 11 July 2011 The maximum entropy method is usually stated in a deceptively simple way: from among all the probability distributions compatible with empirical data, pick the one with the highest information-theoretic entropy. To really understand where this comes from, and appreciate it at its proper worth, we need to look at its origins in equilibrium statistical mechanics . We start with an assemblage of N particles; they each have a three

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