Mathematical Sciences: Statistical Inference for Some Dynamic and Spatial Phenomena

该项目解决了同时放电的生物神经元阵列的数学表示，目的是根据放电时间推断它们的因果关系或影响图。几种类型的点过程的方法论将被扩展到包括全似然和二阶程序，以扩展社会科学家的路径分析和因果模型的结果。对于两个或三个神经元的小型网络，部分相干分析和阈值建模被证明是有效的；然而，对于具有8个神经元的大型网络的数据，需要进行非平凡扩展以进行显示和分析。生理上，神经元通过脉冲串相互交流，发出的脉冲继续影响其他神经元；神经元本身也会受到影响。这项研究的目的是通过观察单个神经元的放电时间来推断神经元网络的连接线或“接线图”。

This project addresses the mathematical representation of arrays of biological neurons that are firing simultaneously with the goal of inferring their causal connections or influence diagram on the basis of firing times. The methodology of point processes of several types will be extended to include full likelihood and second-order procedures to extend the results from social scientists' path analysis and causal modeling. For small net works of two or three neurons, partial coherence analysis and threshold modeling have proved effective; however, for data for a larger network with eight neurons, nontrivial extensions are needed for display and for analysis. Physiologically, neurons communicate with each other via spike trains, emitting pulses that go on to influence other neurons; and the neurons are themselves influenced. The goal of this research is to infer the connection lines or "wiring diagram" of a network of neurons by observing their individual firing times.