MCMC METHODS FOR INVERSE PROBLEMS

A major numerical technique in Bayesian statistical analysis is the use of MCMC (Markov chain Monte Carlo) methods that only rather recently have opened the way for proper statistical analysis of nonlinear models. Real-life modelling problems often provide specific challenges for the application of MCMC methods: the problems are high-dimensional, and the number of unknown parameters depends on the numerical discretization of the problem. The problems may include massive, time-dependent data sets that preclude the use of fixed or hand--tuned standard methods, necessitating the use of adaptive MCMC algorithms that have been developed by our group - now an increasingly topical area of Bayesian statistics.


PROJECT DESRIPTION


In national and international collaboration we further develop effective adaptive MCMC methods, especially for
  • Strongly nonlinear and ill-posed parameter estimation problems
  • High-dimensional inverse problems
  • Optimal design of experiments: the MCMC methods provide knowledge of posterior parameter distributions, that in turn can be employed to design informative new measurements
  • Combining MCMC methods with data assimilation problems for time-dependent models

FUNDING


The project receives funding from two sources. We are a part of the Finnish Center of Excellence in Inverse Problems research, nominated by the Academy of Finland. We also belong to the MASI consortium of TEKES (download a PowerPoint presentation in finnish here).