Aspects of recursive Bayesian estimation
This thesis is concerned with the theoretical and practical aspects of some problems in Bayesian time series analysis and recursive estimation. In particular, we examine procedures for accommodating outliers in dynamic linear models which involve the use of heavy-tailed error distributions as alternatives to normality. Initially we discuss the basic principles of the Bayesian approach to robust estimation in general, and develop those ideas in the context of linear time series models. Following this, the main body of the thesis attacks the problem of intractibility of analysis under outlier accommodating assumptions. For both the dynamic linear model and the classical autoregressive-moving average schemes we develop methods for parameter estimation, forecasting and smoothing with non-normal data. This involves the theoretical examination of non-linear recursive filtering algorithms as robust alternatives to the Kalman filter and numerical examples of the use of these procedures on simulated data. The asymptotic behaviour of some special recursions is also detailed in connection with the theory of stochastic approximation. Finally, we report on an application of Bayesian time series analysis in the monitoring of medical time series, the particular problem involving kidney transplant patients.