This project is concerned with Bayesian semi-parametric and fully nonparametric approaches for estimating drift functions in systems of stochastic differential equations (SDEs). We will develop robust and computational efficient sequential Monte Carlo approaches and variational Bayesian methods and will study their convergence rates and approximation properties. We will also derive new methods for Bayesian model selection to decide on the base of available data which prior from a given collection is most appropriate for the SDE estimation problem at hand.
The project will be carried out jointly between the
- TU Berlin, where the focus will be on variational Bayesian methods on combined state and drift estimation for SDEs,
- the Weierstrass-Institut Berlin, where the focus will be on prior selection for semi- and non-parametric statistics applied to SDEs, and
- the University of Potsdam, where the focus will be on sequential Monte Carlo methods for high-dimensional inference problems arising from SDEs.
- Probabilistic Forecasting and Bayesian Data Assimilation
Colin Cotter and Sebastian Reich, Cambridge University Press, 2015
- Variational mean-field algorithm for efficient inference in large systems of SDEs
Michail Vrettas, Manfred Opper and Dan Cornford, Phys. Ref. E. 91:012145, 2015
- Bootstrap tuning of ordered model selection
Vladimir Spokoiny and Niklas Willrich, arXiv:1507.05034, Weierstrass-Institute Berlin, 2015