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Robust, Scalable Ensemble-based Monte Carlo Methods

This page describes a project within the Mathematical Foundations strand of the Lloyds Register Foundation–Alan Turing Institute programme on Data-centric Engineering.

Description

Sequential Monte Carlo and related methods make use of an ensemble of samples in order to approximate a distribution or distributions of interest. In some settings -- particularly, but far from exclusively, those in which it is necessary to process observations as they are received or the approximation of a normalizing constant is of interest -- such methods can provide extremely good performance. These algorithms are well-suited to online inference, but also provide an alternative to Markov chain Monte Carlo for approximating the posterior distribution for Bayesian inference and find numerous applications in the approximation of rare event probabilities.

There are a number of ways in which the scalability of these methods can be improved, and adaptive specification of algorithm parameters can in principle allow for robust and near-automatic application of these methods to broad classes of problems.

Existing application areas are diverse including, for example, neuroimaging, ray-tracing and autonomous navigation as well as the numerical solution of (and uncertainty quantification for) differential equation systems.

People

  • Letizia Angeli (Warwick - Mathematics & Statistics)
  • Theo Damoulas (Warwick - Computer Science)
  • Arnaud Doucet (Oxford - Statistics)
  • Stefan Grosskinsky (Warwick - Mathematics & Complexity Science)
  • Paul Jenkins (Warwick - Computer Science & Statistics)
  • Adam Johansen (Warwick - Statistics)

Preprints

Recent Reports

  1. L. J. Rendell, A. M. Johansen, A. Lee and N. Whiteley. Global consensus Monte Carlo. ArXiv mathematics e-print 1807.09288 [arxiv]
  2. A. Finke, A. Doucet, and A. M. Johansen. Limit theorems for sequential MCMC methods. ArXiv mathematics e-print 1807.01057 [arxiv]
  3. J. Koskela, P. Jenkins, A. M. Johansen, and D. Spanò. Asymptotic genealogies of interacting particle systems with an application to sequential Monte Carlo. ArXiv mathematics e-print 1804.01811 [arxiv]