Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods

The increasing availability of data presents an opportunity to calibrate unknown parameters which appear in complex models phenomena the biomedical, physical and social sciences. However, model complexity often leads parameter-to-data maps are expensive evaluate only available through noisy approximations. This paper is concerned with use interacting particle systems for solution resulting inverse problems parameters. Of particular interest case where forward evaluations subject rapid fluctuations, parameter space, superimposed on smoothly varying large scale parametric structure interest. Multiscale analysis used study behaviour system algorithms when such we refer as noise, pollute dependence map. Ensemble Kalman methods (which derivative-free) Langevin-based derivative map) compared this light. ensemble shown behave favourably presence noise map, whereas Langevin adversely affected. On other hand, have correct equilibrium distribution setting noise-free models, whilst provide uncontrolled approximation, except linear case. Therefore a new class algorithms, Gaussian process samplers, combine benefits both methods, introduced perform favourably.