Advanced Monte Carlo Methods for Inference in Complex Dynamic Models
Lead Research Organisation:
University of Oxford
Department Name: Statistics
Abstract
Many physical phenomena and much data can be accurately modelled using statistical or proba-
bilistic models. Examples include the volatility of the stock market, gene expressions, radar signals,
relational data or images. However, even if it is possible to obtain realistic physical models or satisfactory
statistical models, only the simplest can be solved without the use of numerical methods.
Examples of the need for such numerical methods include non-linear non-Gaussian time series models,
Markov random fields, social networks models and so on. Thanks to the advent of enormous,
cheap computational power and the development of a plethora of complex inference mechanisms, it
is now possible, and in many real world systems it is becoming increasingly common, to employ
sophisticated simulation-based techniques to provide solutions to problems previously deemed
insoluble. The intention behind the research program discussed herein is to extend current, and devise
novel, simulation-based architectures to attack and efficiently solve problems that are still deemed
intractable.
bilistic models. Examples include the volatility of the stock market, gene expressions, radar signals,
relational data or images. However, even if it is possible to obtain realistic physical models or satisfactory
statistical models, only the simplest can be solved without the use of numerical methods.
Examples of the need for such numerical methods include non-linear non-Gaussian time series models,
Markov random fields, social networks models and so on. Thanks to the advent of enormous,
cheap computational power and the development of a plethora of complex inference mechanisms, it
is now possible, and in many real world systems it is becoming increasingly common, to employ
sophisticated simulation-based techniques to provide solutions to problems previously deemed
insoluble. The intention behind the research program discussed herein is to extend current, and devise
novel, simulation-based architectures to attack and efficiently solve problems that are still deemed
intractable.
Planned Impact
The development of advanced Monte Carlo methods for inference has multiple applications in a wide range of fields.
The following applications will be addressed during this research programme
* the development of more powerful methods for data assimilation problems arising in marine and atmospheric contexts.
* the development of efficient Monte Carlo inference methods in financial econometrics (stochastic volatility models) and structural econometrics (auctions models widely used in e-commerce).
* the development of Monte Carlo methods for inference for very large data sets which is becoming crucial in this era of "Big Data".
* the application to social networks analysis. Social networks are increasingly used to help understand phenomena as distinct as the spread of diseases, analyze friendship or corporate networks.
However Monte Carlo methods are already employed in many areas: computer graphics, data assimilation, ecology, econometrics, genetics, robotics, vision, signal processing, tomography, tracking, etc. Any significant development, properly disseminated, in this area should have attract a lot of interest and could have a large impact.
The longer term benefits of this project are also closely linked to the RCUK "Digital Economy" programme. For example the `digital hospital' component of this programme involves the real-time accurate data fusion and tracking of patients. This could directly benefit from the development of the techniques I plan to develop.
The following applications will be addressed during this research programme
* the development of more powerful methods for data assimilation problems arising in marine and atmospheric contexts.
* the development of efficient Monte Carlo inference methods in financial econometrics (stochastic volatility models) and structural econometrics (auctions models widely used in e-commerce).
* the development of Monte Carlo methods for inference for very large data sets which is becoming crucial in this era of "Big Data".
* the application to social networks analysis. Social networks are increasingly used to help understand phenomena as distinct as the spread of diseases, analyze friendship or corporate networks.
However Monte Carlo methods are already employed in many areas: computer graphics, data assimilation, ecology, econometrics, genetics, robotics, vision, signal processing, tomography, tracking, etc. Any significant development, properly disseminated, in this area should have attract a lot of interest and could have a large impact.
The longer term benefits of this project are also closely linked to the RCUK "Digital Economy" programme. For example the `digital hospital' component of this programme involves the real-time accurate data fusion and tracking of patients. This could directly benefit from the development of the techniques I plan to develop.
People |
ORCID iD |
Arnaud Doucet (Principal Investigator / Fellow) |
Publications
Bérard J
(2014)
A lognormal central limit theorem for particle approximations of normalizing constants
in Electronic Journal of Probability
Yildirim S
(2013)
An Online Expectation-Maximization Algorithm for Changepoint Models
in Journal of Computational and Graphical Statistics
Tadic V
(2017)
Asymptotic bias of stochastic gradient search
in The Annals of Applied Probability
Wang L
(2016)
Bayesian Phylogenetic Inference Using a Combinatorial Sequential Monte Carlo Method
in Journal of the American Statistical Association
Heng J
(2020)
Controlled sequential Monte Carlo
in The Annals of Statistics
Bishop A
(2014)
Distributed Nonlinear Consensus in the Space of Probability Measures
in IFAC Proceedings Volumes
Doucet A
(2015)
Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator
in Biometrika
Lienart T
(2015)
Expectation Particle Belief Propagation
Kimura T
(2011)
Expectation-maximization algorithms for inference in Dirichlet processes mixture
in Pattern Analysis and Applications
Deligiannidis G
(2019)
Exponential ergodicity of the bouncy particle sampler
in The Annals of Statistics
Cuturi M.
(2014)
Fast computation of Wasserstein barycenters
in 31st International Conference on Machine Learning, ICML 2014
Maddison C.J.
(2017)
Filtering variational objectives
in Advances in Neural Information Processing Systems
Caron Francois
(2017)
Generalized Polya Urn for Time-Varying Pitman-Yor Processes
in JOURNAL OF MACHINE LEARNING RESEARCH
Heng J
(2021)
Gibbs Flow for Approximate Transport with Applications to Bayesian Computation
in Journal of the Royal Statistical Society Series B: Statistical Methodology
Nevat I
(2014)
Joint Channel and Doppler Offset Estimation in Dynamic Cooperative Relay Networks
in IEEE Transactions on Wireless Communications
Bardenet Remi
(2017)
On Markov chain Monte Carlo methods for tall data
in JOURNAL OF MACHINE LEARNING RESEARCH
Kantas N
(2015)
On Particle Methods for Parameter Estimation in State-Space Models
in Statistical Science
Linde N
(2017)
On uncertainty quantification in hydrogeology and hydrogeophysics
in Advances in Water Resources
Bouchard-Côté, A.
(2017)
Particle gibbs split-merge sampling for Bayesian inference in mixture models
in Journal of Machine Learning Research
Lee Anthony
(2014)
Perfect simulation using atomic regeneration with application to Sequential Monte Carlo
in arXiv e-prints
Bierkens J
(2018)
Piecewise deterministic Markov processes for scalable Monte Carlo on restricted domains
in Statistics & Probability Letters
Yoshida R
(2014)
Preface
in Annals of the Institute of Statistical Mathematics
Yildirim S
(2018)
Scalable Monte Carlo inference for state-space models
Pitt M
(2014)
Simulated likelihood inference for stochastic volatility models using continuous particle filtering
in Annals of the Institute of Statistical Mathematics
Bouchard-Côté A
(2015)
The Bouncy Particle Sampler: A Non-Reversible Rejection-Free Markov Chain Monte Carlo Method
Bouchard-Côté A
(2018)
The Bouncy Particle Sampler: A Nonreversible Rejection-Free Markov Chain Monte Carlo Method
in Journal of the American Statistical Association
Deligiannidis G
(2015)
The Correlated Pseudo-Marginal Method
Deligiannidis G
(2018)
The Correlated Pseudomarginal Method
in Journal of the Royal Statistical Society Series B: Statistical Methodology
Del Moral P
(2015)
Uniform Stability of a Particle Approximation of the Optimal Filter Derivative
in SIAM Journal on Control and Optimization
Description | I have worked on new statistical methods to estimate the state and parameter of complex stochastic systems arising in a wide range of scientific fields such as econometrics, engineering and computational biology. |
Exploitation Route | Some of the methods I have developed are very general and could be used in a very wide range of applications. |
Sectors | Aerospace, Defence and Marine,Digital/Communication/Information Technologies (including Software),Electronics,Energy,Environment,Financial Services, and Management Consultancy |
Description | The 2015 Biometrika paper co-authored with G. Deligiannids, M.K.Pitt and R. Kohn is now highly cited, having received almost 300 citations. In particular, it has been used to tune algorithms to learn the parameters of epidemilogical models, including models for Covid-19 transmission. |
First Year Of Impact | 2020 |
Sector | Aerospace, Defence and Marine,Digital/Communication/Information Technologies (including Software),Financial Services, and Management Consultancy,Healthcare,Pharmaceuticals and Medical Biotechnology |