07.08.2018

Computational statistics and simulation methods

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Many problems in modern statistics (and related areas such as machine learning, engineering and economics) rely on data with substantial variability, missing observations and/or complicated inter-dependencies. Such data is usually best analysed in terms of a large probabilistic model which connects all the observed quantities with the unknowns.

We aim to develop reliable general inference algorithms for such models, without imposing restrictive modelling assumptions. In the Bayesian setting, the most successful algorithms to date are based on sophisticated Monte Carlo simulation methods. Simulation is useful also in likelihood-based inference, where stochastic gradient type optimisation algorithms can be applied.

Main Researchers:

PhD Students:

The group collaborates closely with Stochastic analysis & SDEs
 

Some International Collaborators

Professor Christophe Andrieu (University of Bristol), Professor Gersende Fort (Télécom ParisTech), Dr Anthony Lee (University of Bristol), Professor Eric Moulines (Ecole Polytechnique, Paris), Dr Sumeetpal Singh (University of Cambridge)

Research

Analysis of Monte Carlo algorithms

(Research team: M. Vihola, J. Franks)

We aim to understand theoretically when certain Monte Carlo methods the methods are efficient and why. This allows for methodological development, choosing right methods for right tasks, and tuning the algorithms in an optimal manner.

 

Scalable Monte Carlo

(Research Team: M. Vihola, J. Franks)

Many Monte Carlo methods, including the popular Markov chain Monte Carlo (MCMC), work well with small data sets, but are problematic when data size increases. The project develops new Monte Carlo inference methods, which are suitable with bigger data sets. The methods are designed to be used efficiently with parallel and distributed computing facilities.

Selected publications

  • A. Lee, S. S. Singh and M. Vihola. Coupled conditional backward sampling particle filter, 2018.
  • J. Franks and M. Vihola. Importance sampling correction versus standard averages of reversible MCMCs in terms of the asymptotic variance, 2017.
    arXiv:1706.09873
  • M. Vihola, J. Helske and J. Franks. Importance sampling type estimators based on approximate marginal MCMC, 2016.
    arXiv:1609.02541
  • M. Vihola. Unbiased estimators and multilevel Monte Carlo, Operations Research, 66(2):448–462, 2018. doi:10.1287/opre.2017.1670
  • C. Andrieu and M. Vihola. Establishing some order amongst exact approximations of MCMCs. Annals of Applied Probability. 26(5):2661–2696, 2016. doi:10.1214/15-AAP1158
  • C. Andrieu, A. Lee and M. Vihola. Uniform ergodicity of the iterated conditional SMC and geometric ergodicity of particle Gibbs samplers. Bernoulli 24(2), 842–872, 2018. doi:10.3150/15-BEJ785
  • G. Fort, E. Moulines, A. Schreck and M. Vihola. Convergence of Markovian stochastic approximation with discontinuous dynamics. SIAM Journal on Control and Optimization. 54(2):866–893, 2016. doi:10.1137/140962723
  • C. Andrieu and M. Vihola. Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms. Annals of Applied Probability, 25(2):1030–1077, 2015. doi:10.1214/14-AAP1022
  • C. Andrieu and M. Vihola. Markovian stochastic approximation with expanding projections. Bernoulli, 20(2):545–585, 2014. doi:10.3150/12-BEJ497
  • B. Miasojedow, E. Moulines and M. Vihola. An adaptive parallel tempering algorithm. Journal of Computational and Graphical Statistics 22(3):649–664, 2013. doi:10.1080/10618600.2013.778779
  • M. Vihola. Robust adaptive Metropolis algorithm with coerced acceptance rate. Statistics and Computing 22(5):997–1008, 2012. doi:10.1007/s11222-011-9269-5

Funding

1) Academy of Finland: Exact approximate Monte Carlo methods for complex Bayesian inference (PI Matti Vihola)

2) Academy of Finland: Scalable methods for reliable Bayesian inference (PI Matti Vihola)