Many of the most challenging problems in applied science and engineering demand the construction and interpretation of complex dynamical models, involving latent structures and many degrees of freedom, which are suitable for high-dimensional, heterogeneous temporal data. While common Big-data schemes are associated to distributed storage and computing technologies for the parallel processing of massive data sets, emerging technologies in fields such as personalised medicine , numerical weather prediction or quantitative climate science demand the ability to:

1. Learn from data sets which are strikingly small compared to the dimension of the unknown variables and parameters in the model
2. Devise computationally efficient algorithms for numerical inference (estimation, detection, tracking and prediction).

In this scenario, probabilistic modelling and Bayesian inference are the cornerstones to handle model and prediction uncertainties. Before the big-data parallel processing kicks in, scalable high-dimensional computational modelling and inference tools must be devised, thoroughly understood and properly assessed.

In this project we aim at devising classes of dynamical probabilistic models, with allied computational inference methods, which can be used to solve real-world problems in personalised medicine and quantitative climate prediction. While these two fields may look far apart, the key issues to be addressed in terms of model learning and computational inference are of the same kind. We advocate a common methodological approach to problems in both areas and expect a considerable degree of cross fertilization, with ideas and techniques that appear in one field and then can be successfully exploited in the other.