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Gareth Roberts

Professor Gareth Roberts

Professor Gareth Roberts

Research Fellow

Interests and expertise (Subject groups)

Grants awarded

Solving intractable likelihood problems through exact Monte Carlo methods

Scheme: Wolfson Research Merit Awards

Organisation: University of Warwick

Dates: May 2015-Apr 2020

Value: £60,000

Summary: I work in the areas of theory, methodology and applications of Computational Statistics and Probability. Within my career, my broad background across Probability and Statistics has allowed me to exploit synergies between Stochastic Processes and Statistical Inference; both through a probabilistic understanding of stochastic algorithms used in Statistics; and conversely for carrying out inference for stochastic phenomena modelled as Stochastic Processes. My major area of application involves veterinary and human infectious disease Epidemiology, a diverse area which involves close research collaboration with biologists, veterinary and medical scientists, epidemiologists as well as governmental research agencies tasked with predicting and controlling disease outbreaks. For example 1. stability theory of stochastic algorithms for computational statistics, particularly Markov chain Monte Carlo (MCMC) and sequential Monte Carlo methods and variants; 2. analysis of convergence of MCMC algorithms and its optimisation,especially the framework of optimal scaling, and parameterisation for Gibbs samplers and related Metropolis-Hastings schemes; 3. likelihood-based inference for partially observed Stochastic Processes, especially (jump-) diffusion models, and infinite-dimensional models absolutely continuous with respect to Gaussian measures; 4. theory and methodology for online improving Markov chain-based algorithms using adaptive methods; 5. the development of stochastic algorithms for intractable likelihood problems, especially based on pseudo-marginal methods and the Bernoulli factory; 6. simulation of and Monte Carlo methods for solutions to stochastic differential equations, particularly using discretisation-error-free techniques; 7. introduction of a collection of methodologies for Bayesian inference for partially observed epidemics with applications including foot and mouth disease, bovine tB (see for example my recent Nature paper, and both Human and Avian Influena.

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