Advancing the Geometric Framework for Computational Statistics: Theory, Methodology and Modern Day Applications

The vision of this research is to formalise the geometric foundations of computational statistics and provide the tools and analytic results required to realise the ambition of developing the advanced statistical methodology that is essential to address emerging inference problems of major importance across the sciences and industry. As ever more demanding and ambitious applications of existing statistical inference methods are being considered, the capabilities of computational statistics tools are constantly being stretched, often beyond what is practically feasible. For example the potential to gain insights into the mechanisms of cellular function, elucidating ecological dynamics; improving neurological diagnostics, and uncovering the deep mysteries of the cosmos are only some of the ongoing scientific studies that are heavily reliant on statistical inference methods and are placing unparalleled demand on the current capabilities of available statistical methodology. This situation motivates continual innovation in the development of statistical methods for the quantification of uncertainty. The aim of this proposed research is to be more ambitious and go much further in establishing a novel paradigm that underpins the advancement of next generation computational statistical methods by formalising and developing advanced Monte Carlo methods. The geometric foundations of computational statistics will be formalised within this proposed research in a way that reaches beyond traditional interfaces between statistical and mathematical sciences.

As a major new area of Statistical Science is being established it is important that a community is built and this will be facilitated by organising specific workshops and special interest group meetings at the main international statistics meetings such as ISI, JSM, ISBA, mathematics (e.g. ICMS funded meetings), as well as application domains such as systems biology (ICSB), Computing Science (NIPS and ICML) and general science (Royal Society of London/Edinburgh).

The applicant has been successful in this fashion previously with the organization of the MASAMB meetings where a 'Computational and Systems Biology' research community has been formed and is now expanding and making excellent headway in contributing to the advances being made in modern day biology. More recently he will be organising an ICMS international workshop on Advances in Monte Carlo Methods.

The other way that it can be ensured that beneficiaries can access the outcome of this research will be through the availability of distributed software. The development of commercial quality software is premature at present but distribution of research quality codes will certainly form part of the standard publication process to ensure rapid independent replication of reported results.

The visits of collaborators to the UK from Japan, USA, Canada, France and Italy will be ideal opportunities for them to give talks about their part of the research in this fellowship with the Computational Statistics research group at UCL as well as the wider CSML and national organisations such as the Royal Statistical Society and Statistics, Mathematics and Science department in the main UK universities. Likewise when the applicant visits collaborators sites in the USA and France this will afford opportunities to give talks about the progress of the research at their own institutions (e.g. Harvard University) and beyond. It should be stated explicitly that output from the collaborations will include co-authored papers, future joint grant applications, and co-organised workshops.

Communication of research results at the main conferences will be undertaken by the named PDRA as it is seen as an outstanding way for them to be trained and establish themselves in the Statistics Community (and related ones) as well as build their career in Statistical Methodology.

The research of the applicant has had impact in the core disciplines of Statistical Methodology and Computing Science as can be seen by the number of citations of some of his selected papers. Furthermore his engagement across multiple disciplines has brought the potential of statistical methodology to domains such as biology and neuroimaging. In addition his research has had direct impact on UK industry by way of the number of patents that have emerged from his collaborations with industry and indeed next-generation technologies are now emerging commercially that have at their core some of the methods developed by MG (see letter of support from NCR Labs UK). It is anticipated that this fellowship will provide abundant opportunities to influence a number of areas of research where Statistical Methodology is required to reason under uncertainty.