Methodological Research and Statisitical Modelling in Neuroscience

可以说，大脑是人体中最复杂的器官。大约有1000亿个神经细胞（又称神经细胞）。神经元），每个潜在地连接（通过突触）到成千上万的其他神经元，大脑是相互连接的细胞的复杂网络。这些细胞通过电化学波的序列进行交流，这些电化学波被称为尖峰序列。这项研究计划的重点是多变量，多尺度和贝叶斯扩展的国家的最先进的模型在统计建模的神经尖峰列车。最近的数据采集发展允许实验者同时记录数百个神经元的电活动。这突出了对高效数据可视化方法的需求，以及为神经尖峰序列量身定制的多元统计理论。根据我的主要研究兴趣，即计算神经科学，这个建议集中在四个领域，统一的最终目标是理解大脑中的信息编码过程。特别是，1）我们将开发一个多变量点过程框架（具有重置的多变量Reynoldlam过程），用于分析多个神经尖峰序列，这在生物学上是合理的，在计算上是有效的。2)在（1）中开发的多变量点过程框架内，我们将开发模型来捕获在真实的数据中观察到的过度和不足分散的尖峰活动（相对于泊松）。由于神经尖峰序列的欠分散模型很少见，在文献中也没有得到很好的研究，因此所概述的研究将对该学科产生影响。3)我们将开发多尺度多变量模型，从多个时间尺度捕获神经尖峰模式。这种模式经常在不同大脑区域的真实的数据中（同时）观察到，并且开发统计模型来研究这些数据是必要的。4)我们将开发贝叶斯扩展的方法中提出的前三个研究活动。上述研究活动将建立和扩展我以前对神经尖峰序列分析的工作，并为这个前沿的多学科研究领域的本科生，硕士和博士水平的培训提供极好的机会。

The brain is, arguably, the most sophisticated organ in the human body. With approximately 100 billion nerve cells (a.k.a. neurons), each potentially connected (through synapses) to thousands of other neurons, the brain is a complex network of interconnected cells. These cells communicate through sequences of electrochemical waves, which are called spike trains. This research proposal focuses on multivariate, multiscale, and Bayesian extensions of state-of-the-art models in statistical modelling of neural spike trains. Recent data acquisition developments allow experimentalists to simultaneously record the electrical activity of several hundreds of neurons. This highlights the need for efficient data visualization methods, and multivariate statistical theories tailored for neural spike trains. Following my main research interests, i.e. computational neuroscience, this proposal focuses on four areas unified by the ultimate goal of understanding information coding processes in the brain. In particular, 1) we will develop a multivariate point process framework (multivariate Skellam Process with Resetting) for the analysis of multiple neural spike trains, which is both biologically justifiable and computationally efficient. 2) Within the multivariate point process framework developed in (1), we will develop models to capture over and under dispersed spiking activity (relative to Poisson) observed in real data. Since under-dispersed models for neural spike trains are rare and not well-studied in the literature, the outlined research will be impactful to the discipline. 3) We will develop multiscale multivariate models to capture neural spiking patterns from multiple time scales. Such patterns are frequently observed (simultaneously) in real data across different brain regions, and developing statistical models to study such data are necessary. 4) We will develop Bayesian extensions of the methods proposed in the previous three research activities. The above-mentioned research activities will build on and extend my previous work on the analysis of neural spike trains, and provide excellent opportunities for undergraduate, masters, and doctoral level training in this cutting-edge multidisciplinary research area.