Computational Information Geometry and Model Uncertainty/Neuro-informatics

我的研究计划由两个流派组成：计算信息几何(CIG)和神经信息学(NI)。信息几何(IG)是几何学(微分几何、凸几何、仿射几何、代数几何以及Hilbert和Banach空间的无限维几何)在统计理论发展中的应用。计算信息几何学这个术语的意思是，重点是为统计用户生产计算工具。流程一：从长远来看，CIG将制定的方法有可能改变统计做法。该分项目(CIG：1)处理发展统计模型评估工作中普遍存在的一个问题，即建立模型、敏感性和不确定性。它给出了一种计算和实用的方法来实现Box的科学观，他在1976年的里程碑式的论文《科学与统计》中提出了这一观点。在这些论文中，科学知识被认为是通过“理论和实践之间有动力的迭代”、“有效的科学迭代显然需要不受阻碍的反馈”来推进的，并补充说：“由于所有模型都是错误的，科学家必须警惕哪些是重大错误。”因此，我们正在开发可操作的计算工具，以实现这些强大的想法。这些工具都有一个基本的几何背景。子项目(CIG：2)结合了IG的进展和马尔可夫链蒙特卡罗(MCMC)理论方面的一些非常令人兴奋的新工作。这将允许在非常复杂的现实世界问题中进行推理，特别是那些从根本上是高维的和/或具有强非线性约束的问题。流II：神经信息学涉及对来自神经科学的数据使用统计方法，在本应用中，我们将重点放在所谓的脉冲训练数据上。人脑由数十亿个称为神经元的细胞组成，这些细胞通过称为动作电位的电化学波相互通信。这些也被称为尖峰，因为它们往往在时间上非常局部化，时间尺度通常在几毫秒左右。由单个神经元产生的这些神经棘波的序列被称为棘波序列。尖峰列车用来编码信息的机制(S)引起了人们的极大兴趣，这一机制的完整特征仍远未确定。这个项目的目的是使用统计方法来准确地解决这个问题。除了解决纯粹的神经科学问题，理解棘波训练也有重要的应用，如假肢的控制。该项目(NI：神经信息学)由许多较小的、基本上独立的子项目组成，包括：(NI：1可视化)-为多个脉冲训练数据开发数据可视化工具。现代的棘波训练数据可以包括来自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。数据可视化工具将对使用这些数据的从业者非常有用。(NI：2稳健性)-分析通常在脉冲训练数据中发现的测量和分类错误的影响。(NI：3分散)-了解棘波序列的潜在变异性也是对此数据建模的关键部分，将开发新的方法来实现这一点。(NI：4相)-尖峰信号相对于周期信号的激发时间称为相控编码。我们着眼于多个棘波序列的时变阶段的分析和建模。这两个流将在两个重要但不同的领域推进统计方法：基础理论和神经科学应用。他们将为HQP提供高质量的培训，在学术界和更广泛的领域都有强烈的需求。

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.