Inferring document relevance from incomplete information Javed A. Aslam , Emine Yilmaz. References Publications referenced by this paper. On the rationale of maximum-entropy methods E.
Space-Time Power Spectral Analysis Using the Maximum Entropy Method
The probability of any particular result is the multinomial distribution ,. She decides to maximize.
Using Stirling's approximation , she finds. All that remains for the protagonist to do is to maximize entropy under the constraints of her testable information.
She has found that the maximum entropy distribution is the most probable of all "fair" random distributions, in the limit as the probability levels go from discrete to continuous. Giffin and Caticha state that Bayes' theorem and the principle of maximum entropy are completely compatible and can be seen as special cases of the "method of maximum relative entropy". They state that this method reproduces every aspect of orthodox Bayesian inference methods. In addition this new method opens the door to tackling problems that could not be addressed by either the maximal entropy principle or orthodox Bayesian methods individually.
Moreover, recent contributions Lazar , and Schennach show that frequentist relative-entropy-based inference approaches such as empirical likelihood and exponentially tilted empirical likelihood — see e.
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Owen and Kitamura can be combined with prior information to perform Bayesian posterior analysis. Jaynes stated Bayes' theorem was a way to calculate a probability, while maximum entropy was a way to assign a prior probability distribution. It is however, possible in concept to solve for a posterior distribution directly from a stated prior distribution using the principle of minimum cross entropy or the Principle of Maximum Entropy being a special case of using a uniform distribution as the given prior , independently of any Bayesian considerations by treating the problem formally as a constrained optimisation problem, the Entropy functional being the objective function.
For the case of given average values as testable information averaged over the sought after probability distribution , the sought after distribution is formally the Gibbs or Boltzmann distribution the parameters of which must be solved for in order to achieve minimum cross entropy and satisfy the given testable information. The principle of maximum entropy bears a relation to a key assumption of kinetic theory of gases known as molecular chaos or Stosszahlansatz.
This asserts that the distribution function characterizing particles entering a collision can be factorized. Though this statement can be understood as a strictly physical hypothesis, it can also be interpreted as a heuristic hypothesis regarding the most probable configuration of particles before colliding. From Wikipedia, the free encyclopedia.
This article is about the probability theoretic principle. For the classifier in machine learning , see maximum entropy classifier. For other uses, see maximum entropy disambiguation. Principle in Bayesian statistics. This article includes a list of references , but its sources remain unclear because it has insufficient inline citations.
Please help to improve this article by introducing more precise citations. September Learn how and when to remove this template message. Main article: maximum entropy probability distribution. Physical Review. Series II. Bibcode : PhRv.. Journal of Econometrics.
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