Tsallis最大熵原理及其逆问题
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摘要
首先研究并证明了Tsallis最大熵和约束条件下的Tsallis最大熵原理;其次,针对最大熵方法的逆问题,讨论了贝叶斯参数估计理论中利用Tsallis最大熵原理确定参数的先验概率的逆问题;对于一些具体的概率分布,根据Tsallis最大熵原理,利用变分的方法,求解出使Tsallis熵达到最大值的约束条件.该类逆问题的解一般不是惟一的,其他分布情况也可按此方法得出。
First,we have studied and proved the Tsallis maximum entropy principle and the Tsallis maximum entropy principle under the constraint conditions. Secondly,in view of the inverse problem of the maximum entropy method,the inverse problem of using the Tsallis maximum entropy principle to determine the prior probabilities in the Bayesian parameter estimation theory is discussed. For some specific probability distributions,the Tsallis maximum entropy principle and variation principle are used to solve the constraint conditions that maximize the Tsallis entropy. The solution of this inverse problem is generally not unique,and other distributions can also be obtained by this method.
First,we have studied and proved the Tsallis maximum entropy principle and the Tsallis maximum entropy principle under the constraint conditions. Secondly,in view of the inverse problem of the maximum entropy method,the inverse problem of using the Tsallis maximum entropy principle to determine the prior probabilities in the Bayesian parameter estimation theory is discussed. For some specific probability distributions,the Tsallis maximum entropy principle and variation principle are used to solve the constraint conditions that maximize the Tsallis entropy. The solution of this inverse problem is generally not unique,and other distributions can also be obtained by this method.
引文
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[11]WU Y J.Probability Theory and Two Questions in Srochastic Process[D].Daqing:Northeast Petroleum University,2015
[2]TSALLIS C.Possible Generalization of Boltzmann Gibbs Statistics[J].J Stat Phys 1988,52(1-2):479-487
[3]PLASTINO A R,Plastino A.Non-Extensive Statistical Mechanics and Generalized Fokker-Planck Equation[J].Physica A:Statistical Mechanics and Its Applications,1995,222(1-4):347-354
[4]CARUSO F,TSALLIS C.Nonadditive Entropy Reconciles the Area Law in Quantum Systems with Classical Thermodynamics[J].Physical Review E,2008,78(2):1-6
[5]JAYNES E T.Papers on Probability,Statistics and Statistical Physics[J].Dordrecht:Kluwer,1989(38):87-124
[6]LIU C S.Maximal Nonsymmetric Entropy Leads Naturally to Zip’s Law[J].Fractals-Complex Geometry Pattems&Scalling,2008,16(1):99-101
[7]LIU C S.Nonsymmetric Entropy and Maximum Nonsymmetric Entropy Principle[J].Chaos Solitons&Fractals,2009,40(5):2469-2474
[8]MAO S S.Bayes Statistics[M].Beijing:China Statistic Publishing House,2005
[9]ZHANG Y T,CHEN H F.Bayes Parameter Inferenc[M].Beijing:Science Press,1991
[10]WAN H H.Bayes Parameter Estimation of Invers Problem of Maximum Entropy Method[J].Joumal o Northeast Petroleum University,2012,36(6):101-103
[11]WU Y J.Probability Theory and Two Questions in Srochastic Process[D].Daqing:Northeast Petroleum University,2015