Computational statistics and simulation methods


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.

The group collaborates with applied researchers, seeking for interesting applications with inferential challenges. We are always interested in new challenges!

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 topics


Modelling of animal movements

We collaborate with researchers of Natural Resources Institute Finland (Luke) aiming to understand animal movements and populations. 

Analysis of Monte Carlo algorithms

We seek theoretical understanding about when certain Monte Carlo 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

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

  • M. Vihola and J. Franks. On the use of ABC-MCMC with inflated tolerance and post-correction, 2019.
  • J. Franks, A. Jasra, K. Law and M. Vihola. Unbiased inference for discretely observed hidden Markov model diffusions, 2018.
  • 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.
  • M. Vihola, J. Helske and J. Franks. Importance sampling type estimators based on approximate marginal MCMC, 2016.
  • F. Lindsten, J. Helske and M. Vihola. Graphical model inference: Sequential Monte Carlo meets deterministic approximations, Advances in Neural Information Processing Systems 31, 2018.
  • 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


  • Academy of Finland: Scalable methods for reliable Bayesian inference (2018-2022, PI Matti Vihola)
  • Academy of Finland: Exact approximate Monte Carlo methods for complex Bayesian inference (2014-2019, PI Matti Vihola)