The aim of the module is to introduce methods for constructing stochastic models of dynamical systems and learning their parameters from measurements of input and output signals. The module also covers basic techniques for prediction of unknown quantities exploiting available sensor data.

Upon completion of the module, you will be able to: 1- construct discrete-time stochastic models of dynamical systems; 2- calculate parameters in stochastic models from input/output data; 3- develop and devise prediction algorithms making use of data provided by sensors, as well as historical data; 4- assess the quality of parameter estimates in stochastic models.

Stochastic dynamical systems and their description in terms of standard discrete time models; these include, for example, linear difference equation models known as ARMAX (Autoregressive Moving Average models with Exogenous input) model; Basics of estimation and learning theory; Least-squares parameter estimation; The statistical properties of parameter estimates; Recursive algorithms for parameter identification; Sources of parameter bias; The effects of over-parameterization; Techniques for selecting model order.