Computational Information Geometry and Model Uncertainty/Neuro-informatics

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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.