Statistical Inverse Problem and its Applications to Complex Systems

本文利用基于反馈系统理论的辨识方法，研究了脑功能或工程对象等复杂系统的统计逆问题。自从上个世纪人们对大脑活动的局部化有了很好的了解以来，大脑中相关区域的活动在本世纪引起了人们对更高阶大脑功能，即语言、识别、视觉活动的兴趣。在研究之初，对于脑磁图(MEG)的时间序列数据似乎很难攻击这些主题，因为大脑中存在许多活动的并行处理。然而，反复的电或声刺激会在大脑中产生周期性的活动，这些活动被诱发的磁场称为。然后，利用基于时间结构的独立分量分析方法，将特定的诱发磁场与脑背景磁场分离。一个例子是听觉诱发领域，另一个是体感诱发领域。在选择诱发脑磁图后，可以利用基于反馈系统理论的辨识方法来检验脑磁图时间序列数据中包含的动力学信息。即辨识可观测通道之间的传递函数，并得到它们的冲激响应。它们为我们提供了大脑各区域之间的动力。该方法框架内的高斯性对于获得时间序列数据的平稳性具有重要意义，因为它不仅存在于核磁共振数据中，而且还存在于核电站中子数的波动中。

In this research statistical inverse problem on complex systems such as brain functions or engineering plants is examined by using the identification method based on feedback system theory. Since the localization of brain activities was well understood in the last century, activities of associated regions in brain are interested for understanding of higher order brain functions, i.e., language, recognition, vision activities, in the present century.At the beginning of research, it seemed to be difficult to attack such topics for time series data of magnetoencephalography (MEG), since there are many parallel processing of activities in brain. However, repeated electrical or sound stimuli give periodical activities in brain, and they are called by the evoked magnetic field. Then, we could separate particular evoked magnetic fields from background magnetic fields of brain by using the independent component analysis based on temporal structure. One example is the auditory evoked field, and the other is the somatosensory evoked field. After selection of evoked MEG we can examine dynamics included in MEG time series data by the identification method based on feedback system theory. That is, transfer functions between observable channels were identified, and their impulse responses were obtained. They give us dynamics between regions of brains. The Gaussianity in the framework of the method was important to obtain the stationarity of time series data, since it is observed in not only MEG data but also fluctuations of neutron number of nuclear power plants.