Computational Information Geometry and Model Uncertainty/Neuro-informatics

我的研究计划包括两个流：计算信息几何（CIG）和神经信息学（NI）。**信息几何（IG）是应用几何（微分、凸、仿射、代数以及希尔伯特和巴拿赫空间的无限维几何）来推进统计理论。术语计算信息几何意味着重点是为统计用户生产计算工具。**流程一：从长远来看，将在CIG中开发的方法有可能改变统计实践。子项目（CIG:1）解决了统计模型评估发展中普遍存在的问题，即模型构建、敏感性和不确定性。它提供了一种计算和实用的方法来实现Box在他1976年具有里程碑意义的论文“科学与统计”中提出的科学观。在这些论文中，科学知识被认为是通过“理论和实践之间的有动机的迭代”，“有效的科学迭代显然需要不受阻碍的反馈”，并补充说：“既然所有的模型都是错误的，科学家必须警惕什么是重要的错误。”因此，我们正在开发可操作的计算工具来实现这些强大的想法。这些工具都有一个潜在的几何背景。子项目（CIG:2）结合了IG的进展和一些非常令人兴奋的马尔可夫链蒙特卡罗（MCMC）理论的新工作。这将允许在非常复杂的现实世界问题中进行推理，特别是那些基本上是高维和/或具有强非线性约束的问题。**流II：神经信息学涉及使用统计方法从神经科学的数据，在这个应用程序中，我们专注于所谓的尖峰列车数据。人类的大脑由数十亿个被称为神经元的细胞组成，这些细胞通过被称为动作电位的电化学波相互交流。这些也被称为尖峰，因为它们往往在时间上非常有限，时间尺度通常在几毫秒左右。由单个神经元产生的一系列神经尖峰被称为尖峰序列。刺突序列用来编码信息的机制引起了极大的兴趣，而对这一机制的完整描述仍远未确定。这个项目的目的是使用统计方法来解决这个问题。除了解决纯粹的神经科学问题，理解突刺神经也有重要的应用，比如假肢的控制。**该项目（NI：神经信息学）由许多较小的，很大程度上独立的子项目组成，包括：（NI:1可视化）-为多个尖峰列车数据开发数据可视化工具。现代的脉冲序列数据可以包括大量相互关联的神经元的记录，显示出许多不同时间尺度上的结构。数据可视化工具对于处理这些数据的从业者来说非常有用。（NI:2鲁棒性）-测量和分类误差的影响分析，通常在尖峰列车数据中发现。（NI:3色散）-理解脉冲序列的潜在可变性也是建模该数据的关键部分，将开发新的方法来做到这一点。（NI:4相位）-相对于周期信号的尖峰触发时间称为相位编码。我们着眼于多尖峰列车时变相位的分析和建模。**两个流将推进统计方法在两个重要的，但不同的领域：基础理论和应用到神经科学。他们将在学术界和更广泛的领域提供高质量的HQP培训，这些领域有强烈的需求。

My research program is comprised of two streams: Computational Information Geometry (CIG) and Neuroinformatics (NI).**Information Geometry (IG) is the application of geometry (differential, convex, affine, algebraic and the infinite dimensional geometries of Hilbert and Banach spaces), to the advancement of statistical theory. The term Computational Information Geometry means the focus is on producing computational tools for users of statistics. **Stream I: The methodology to be developed in CIG has, in the long term, the potential to change statistical practice. The sub-project (CIG:1) tackles a ubiquitous problem of the development of assessment of statistical models, i.e., model building, sensitivity and uncertainty. It gives a computational and practical way of implementing Box's view of science, put forward in his landmark 1976 paper 'Science and Statistics'. In these papers, scientific knowledge is seen as advancing by 'a motivated iteration between theory and practice', 'efficient scientific iteration evidently requiring unhampered feedback', adding that: 'since all models are wrong the scientist must be alert to what is importantly wrong.' We are therefore developing operational, computation tools to implement these powerful ideas. These tools all have an underlying geometric background. The sub-project (CIG:2) combines advances in IG and some very exciting new work in Markov chain Monte Carlo (MCMC) theory. This will allow inference in very complex real world problems, in particular ones which are fundamentally high dimensional and/or have strong non-linear constraints. **Stream II: Neuroinformatics involves the use of statistical methods to data from neuroscience and in this application we focus on so-called spike train data. The human brain consists of billions of cells, called neurons, which communicate with each other through electrochemical waves called action potentials. These are also known as spikes as they tend to be very localized in time, with a time scale typically around a few milliseconds. A sequence of these neural spikes generated by an individual neuron is called a spike train. The mechanism(s) that spike trains use to code information is of great interest and the complete characterization of this mechanism is still far from settled. This project is aimed using statistical methods to address precisely this question. In addition to addressing pure neuroscience questions, understanding spike trains is also has important applications such as the control of prosthetic limbs. **The project, (NI: Neuroinformatics), is comprised of a number of smaller, largely independent, sub-projects and consisting of: (NI:1 Visualisation) - developing data visualisation tools for multiple spike train data. Modern spike train data can include recordings from large numbers of interrelated neurons, showing structure over many different time scales. Data visualisation tools will be extremely useful for practitioners working with this data. (NI:2 Robustness) - the analysis of the effect of measurement and classification errors which are typically found in spike train data. (NI:3 Dispersion) - understanding the underlying variability of spike trains is also a critical part of modelling this data and new methodology will be developed to do this. (NI:4 Phase) - the firing times of spikes relative to a periodic signal is called phased coding. We look at the analysis and modelling of time varying phases for multiple spike trains.**Both streams will advance statistical methodology in two important, but distinct, areas: foundational theory and applications to neuroscience. They will provide high quality training for HQP in areas where there is a strong demand, both in academia and much more widely.