Advancing the Geometric Framework for Computational Statistics: Theory, Methodology and Modern Day Applications
Lead Research Organisation:
University College London
Department Name: Statistical Science
Abstract
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.
Planned Impact
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.
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.
People |
ORCID iD |
Mark Girolami (Principal Investigator / Fellow) |
Publications
Ellam L
(2016)
A Bayesian approach to multiscale inverse problems with on-the-fly scale determination
in Journal of Computational Physics
Cockayne J
(2018)
A Bayesian Conjugate Gradient Method
Betancourt M
(2017)
A Conceptual Introduction to Hamiltonian Monte Carlo
Ellam L
(2017)
A determinant-free method to simulate the parameters of large Gaussian fields
in Stat
Sherrard-Smith E
(2017)
A novel model fitted to multiple life stages of malaria for assessing efficacy of transmission-blocking interventions.
in Malaria journal
Barp A
(2022)
A Riemann-Stein kernel method
in Bernoulli
Betancourt Michael
(2015)
A Unified Treatment of Predictive Model Comparison
in arXiv e-prints
Betancourt M. J.
(2014)
Adiabatic Monte Carlo
in arXiv e-prints
Weber Sebastian
(2016)
Bayesian aggregation of average data: An application in drug development
in arXiv e-prints
Weber S
(2018)
Bayesian aggregation of average data: An application in drug development
in The Annals of Applied Statistics
Oates C
(2019)
Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment
in Journal of the American Statistical Association
Chkrebtii O
(2016)
Bayesian Solution Uncertainty Quantification for Differential Equations
in Bayesian Analysis
Chkrebtii Oksana A.
(2013)
Bayesian Solution Uncertainty Quantification for Differential Equations
in arXiv e-prints
Vermeulen R
(2019)
Constituents of Household Air Pollution and Risk of Lung Cancer among Never-Smoking Women in Xuanwei and Fuyuan, China.
in Environmental health perspectives
Oates C
(2017)
Control Functionals for Monte Carlo Integration
in Journal of the Royal Statistical Society Series B: Statistical Methodology
Oates C
(2014)
Control functionals for Monte Carlo integration
Oates C.J.
(2016)
Control functionals for quasi-monte carlo integration
in Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, AISTATS 2016
Oates C
(2019)
Convergence rates for a class of estimators based on Stein's method
in Bernoulli
Betancourt M
(2015)
Current Trends in Bayesian Methodology with Applications
Mejia Pedro
(2015)
Dietary restriction protects against experimental cerebral malaria via leptin modulation and T-cell mTORC1 suppression
in Nature Communications
Kim Y
(2015)
Electrostatically transparent graphene quantum-dot trap layers for efficient nonvolatile memory
in Applied Physics Letters
Lan S
(2016)
Emulation of higher-order tensors in manifold Monte Carlo methods for Bayesian Inverse Problems
in Journal of Computational Physics
Betancourt M
(2013)
Hamiltonian Monte Carlo for Hierarchical Models
Hurley P
(2017)
HELP: xid+, the probabilistic de-blender for Herschel SPIRE maps
in Monthly Notices of the Royal Astronomical Society
Betancourt Michael
(2016)
Identifying the Optimal Integration Time in Hamiltonian Monte Carlo
in arXiv e-prints
Livingstone S
(2014)
Information-Geometric Markov Chain Monte Carlo Methods Using Diffusions
in Entropy
Livingstone S
(2014)
Information-geometric Markov Chain Monte Carlo methods using Diffusions
Xifara T
(2014)
Langevin diffusions and the Metropolis-adjusted Langevin algorithm
in Statistics & Probability Letters
Lan S
(2015)
Markov Chain Monte Carlo from Lagrangian Dynamics.
in Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
Stathopoulos V
(2013)
Markov chain Monte Carlo inference for Markov jump processes via the linear noise approximation.
in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
Edlow AG
(2014)
Maternal obesity affects fetal neurodevelopmental and metabolic gene expression: a pilot study.
in PloS one
Lyne Anne-Marie
(2013)
On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods
in arXiv e-prints
Lyne A
(2015)
On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods
in Statistical Science
Livingstone S
(2019)
On the geometric ergodicity of Hamiltonian Monte Carlo
in Bernoulli
Livingstone Samuel
(2016)
On the Geometric Ergodicity of Hamiltonian Monte Carlo
in arXiv e-prints
Oates C
(2019)
Optimality Criteria for Probabilistic Numerical Methods
Betancourt M. J.
(2014)
Optimizing The Integrator Step Size for Hamiltonian Monte Carlo
in arXiv e-prints
Briol F
(2019)
Probabilistic Integration: A Role in Statistical Computation?
in Statistical Science
Hennig P
(2015)
Probabilistic numerics and uncertainty in computations.
in Proceedings. Mathematical, physical, and engineering sciences
Ellam L
(2018)
Stochastic Modelling of Urban Structure
Ellam L
(2018)
Stochastic modelling of urban structure.
in Proceedings. Mathematical, physical, and engineering sciences
Sherrard-Smith E
(2018)
Synergy in anti-malarial pre-erythrocytic and transmission-blocking antibodies is achieved by reducing parasite density.
in eLife
Oates C
(2016)
The Controlled Thermodynamic Integral for Bayesian Model Evidence Evaluation
in Journal of the American Statistical Association