Likelihood and Bayesian Prediction of Chaotic Systems
Likelihood and Bayesian Prediction of Chaotic Systems
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混沌系统的似然和贝叶斯预测
DOI：
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发表时间：
1991
期刊：
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通讯作者：
L. Mark Berliner
中科院分区：
文献类型：
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作者：
L. Mark Berliner
摘要最近，在应用学科和数学，以及在科普文献中，在非线性动力系统和混沌过程的领域有相当大的兴趣。所谓非线性、确定性动力系统，我们指的是一个时间序列，其中从某个初始条件开始，序列的值是先前状态的某个固定的非线性函数。这些模型的一个更有趣的方面是，即使在分析简单模型时，它们也倾向于显示非常复杂的、显然是随机的行为。这种混沌行为的后果是很难预测混沌系统的确切行为。预测的困难源于这样一个事实，即使是最微小的错误，包括计算机的错误，无论是在函数的规范还是初始条件中，都可能导致预测的巨大错误。在简要回顾了动力系统和概率在处理不确定性中的作用后，一个com.
Abstract There has recently been considerable interest in both applied disciplines and in mathematics, as well as in the popular science literature, in the areas of nonlinear dynamical systems and chaotic processes. By a nonlinear, deterministic dynamical system, we mean a time series in which, starting at some initial condition, the values of the series are some fixed, nonlinear function of the previous states. One of the more intriguing aspects of these models is their propensity for displaying very complex, apparently random behavior, even when simple models are analyzed. A consequence of such chaotic behavior is that it is difficult to predict the exact behavior of a chaotic system. The difficulty in prediction stems from the fact that even the tiniest of errors, including computer roundoff, in either the specification of the function or the initial condition, can lead to huge errors in prediction. After a brief review of dynamical systems and the role of probability in dealing with uncertainty, a com...