Advanced Monte Carlo Methods for Inference in Complex Dynamic Models

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.

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.