Intractable Likelihood: New Challenges from Modern Applications (ILike)

In most statistical contexts, it is recognised that inference methodology based on the likelihood function are usually methods of choice. However such methods are not always easy to implement. For instance, in complex problems often with massive data sets, it can sometimes be completely impossible to even evaluate the likelihood function. The computational statistics revolution of the 1990s provided powerful methodology for carrying out likelihood-based inference, including Markov chain Monte Carlo methods, the EM algorithm, many associated optimisation techniques for likelihoods, and Sequential Monte Carlo methods.

Although these methods have been and are highly successful in making likelihood-based inference accessible to a wide range of problems from virtually every area of science and technology, we now have a far better understanding of their limitations, for example in high-dimensional problems and for massive data sets. Thus many challenging statistical inference problems of the 21st century cannot be addressed using existing likelihood-based methods. Examples which motivate the current project come from genetics, genomics, infectious disease epidemiology, ecology, commerce, and bibliometrics.

However there have been various recent breakthroughs in computational and statistical approaches to intractable likelihood problems, including pseudo-marginal and particle MCMC, likelihood-free methods such as Approximate Bayesian Computation, composite and pseudo-likelihoods, new simulation methods for hitherto intractable stochastic models, and adaptive Monte Carlo methods. These advances coupled with developments in multi-core computational technologies such as GPUs, have enormous potential for extending likelihood methods to meet the most difficult challenges of modern scientific questions.

All these new areas have demonstrated considerable promise. However, a unified approach is required to deliver a step change in our capability to implement likelihood. The Ilike workplan will initially involve the investigation of 10 projects all combining two or more of the about breakthrough areas.
The second half of the project will involve a similar workplan informed by the outcomes of the initial projects.

The potential impact of the ILike research is substantial due to the fact that the statistical methods are, and can be, used within a range of scientific and industrial applications. We identify four specific pathways to impact:

Dissemination and Publicity

Medium and long term impact of the grant will be achieved by continued and sustained publication in top statistics and application journals, and presentation
at appropriate statistics and application area conferences. Co-ordination of dissemination activities will be key throughout the project. In order to catalyse impact to the research community at large, conference attendance by either investigators or appointed RAs will carry with it a responsibility of reporting the research accomplishments of the grant as a whole, as far as this is possible within the constraints of the particular meeting.

The above will be supplemented by specific activities organised by Ilike, e.g. the EPSRC Science and Innovation awards in Statistics at Warwick and Bristol (CRiSM and SuSTaIn) and their respective strategies of high profile activities. We will organise annual open workshops on New Directions for Likelihood showcasing our research, and acquiring up-to-date information on the latest global developments.

We will also run two Winter schools in Ilike, aimed at early career statisticians, and especially 2nd and 3rd year PhD students. These will help make the use of methods developed in ILike more routine for the next generation of statistical researchers and end-users (including students who will pursue industrial career paths).

Impact of our research will be further amplified through an intensive four week programme around three years into the grant, to which we will invite many world experts in computational likelihood methods. We intend to apply to the Isaac Newton Institute to host this meeting.

We will also publicise our research through a dedicated web-site, making our work readily accessible to all, and giving a focus on highlighting key research ideas, and their application, in a way that is accessible to non-statistical researchers.

Supply of People

The programme grant will train at least 5 new researchers who will be expert in modern statistical methods and their application, and help address the current, widely acknowledged, skills-shortage in this area. Many more will benefit from knowledge gained from our workshops and conferences.

Software and Accessibility of Research

In order to maximise the impact of new computational statistical methods, we will make software implementing new methods freely available via the ILike website. The form this software takes will vary, as appropriate. For example, methods which allow inference for specific models or applications will be developed as R packages. For more generic algorithmic methods we will make available demo software: implementations of the algorithm for different exemplar problems. This will supplement our making details of all research freely available through publishing of pre-prints and technical reports on the website.

Interaction with end-users

Our targeted example application areas (statistics of large-scale directed networks in ecology, commerce, bibliometrics, genetic and genomics and infectious disease epidemiology) are chosen because of our collective track record of applied work in those areas which has made a substantial scientific impact. To catalyse dissemination to these areas, we will feed developments from our methodological work directly through to our current projects in those areas (for example through our current various grants in these areas from BBSRC, MRC, ESRC, EU FP7, NIHR, Wellcome Trust).

We will also use the Ilike grant to launch major application-focussed proposals (such as in Statistics Genetics to the MRC, or in Infectious Disease Epidemiology to the ERC), thus providing secondary benefits to user communities.