Breadcrumb

New developments in Monte Carlo simulation

Supervisor: Christophe Andrieu

Theme: Monte Carlo Computation

Modern statistics and related areas very often require the numerical approximation of quantities that are crucial to the understanding of scientific problems as diverse as target tracking, wireless communications, epidemiology or genomics to name a few. The Monte Carlo (MC) method can be traced back to Babylonian and Old Testament times, but has been systematically used and known under this name since the times of the "Los Alamos School" in the 40's-50's. The method is by nature probabilistic and has proved to be a very efficient tool to approximate quantities of interest in various scientific areas. It is only in the late 80's early 1990's that it was realised by statisticians that the method could be applied to solve many of their problems, and since then the field has seen major developments, both at a methodological and theoretical level. The impact on statistics and related areas has been and is still phenomenal. Current methods have allowed one to significantly push the boundaries of the class of problems that can be routinely tackled using a simple PC computer, but it is recognised that new challenges arising from the "data revolution" in particular will require new methods. The projects outlined below are at the forefront of current research in the area and can be pitched so that they involve either methodological or theoretical work, or both. Working in this area is a particularly nice opportunity to use probabilistic and statistical ideas to develop and analyse new methods which can be useful in many areas of science. Possible areas of research include:
1. Adaptive Monte Carlo algorithms,
2. Markov chain MC, Sequential MC methods or population MC methods,
3. Automatic design of transdimensional MCMC algorithms,
4. Expected auxiliary variable approach (biased and unbiased approximations of ideal algorithms),
5. Methodogy for particle filtering (e.g. static parameter estimation, design of the importance sampling distribution),
6. Optimisation using simulated annealing and stochastic optimisation.


Publications

  • On the ergodicity properties of some adaptive MCMC algorithms (2006)
    C. Andrieu and E. Moulines
    Annals of Applied Probability, vol: 16, Issue: 3
  • Stability of stochastic approximation under verifiable conditions (2005)
    C. Andrieu, É. Moulines and P. Priouret
    SIAM Journal on Control and Optimisation, vol: 44, Issue: 1, Pages: 283 - 312
  • Particle Filtering for Partially Observed Gaussian State Space Models (2002)
    C. Andrieu and A. Doucet
    J. Royal Statist. Soc. B (Methodological), vol: 64, Issue: 4, Pages: 827 - 836