Dynamic models offer a powerful framework for the modelling and analysis of time series, especially noisy time series, which are subject to abrupt changes in pattern. They are used in many time series applications from finance and econometrics, to biological series used in clinical monitoring. In this thesis we describe in detail how dynamic models can be used to model time series, following work from West and Harrison. In particular, we will focus our attention to a specific problem of monitoring kidney failure in patients that have just had cardiac surgery. This work is in joint collaboration with the cardiac surgery unit at the University Hospital of South Manchester. The particular problem studied is that of developing an on-line statistical procedure to monitor the progress of kidney function in individual patients who have recently had heart surgery
