The seamless integration of large data sets into computational models provides one of the central challenges for the mathematical sciences of the 21st century. When the computational model is based on dynamical systems and the data is time ordered, the process of combining data and models is called data assimilation. Historically, the field has been primarily developed by practitioners from meteorology who face the problem of initialising weather prediction models by combining observational data and past forecasts in an optimal way. In this context, data assimilation should be viewed as a high-dimensional, non-stationary statistical inverse problem subject to complex model and data errors. The course will provide an introduction to the mathematical and algorithmic foundations of modern data assimilation methodologies. The first part of the course will cover the mathematical principles of deterministic and probabilistic approaches to state estimation in the context of filtering and smoothing. The second part will be devoted the recent algorithmic advances on sequential Monte Carlo methods for state and parameter estimation. The final third part will cover methods for dealing with misspecified models and model comparison.
Introductory reading:  Kody Law, Andrew Stuart, Konstantinos Zygalakis, Data Assimilation -- A Mathematical Introduction, Springer-Verlag, 2015  Sebastian Reich and Colin Cotter, Probabilistic Forecasting and Bayesian Data Assimilation, Cambridge University Press, 2015
Block Course Dates
September / Early October 2017.