Markov Chain Monte Carlo in Conditionally Gaussian State Space Models

Introduction Linear Gaussian state space models are used extensively, with unknown parameters usually estimated by maximum likelihood: Wecker & Ansley (1983), Harvey (1989). However, many time series and nonparametric regression applications, such as change point problems, outlier detection and switching regression, require the full generality of the conditionally Gaussian model: Harrison & Stevens (1976), Shumway & Stoffer (1991), West & Harrison (1989), Gordon & Smith (1990). The presence of a large number of indicator variables makes it difficult to estimate conditionally Gaussian models using maximum likelihood, and a Bayesian approach using Markov chain Monte Carlo appears more tractable. We propose a new sampler, which is used to estimate an unknown function nonparametrically when there are jumps in the function and outliers in the observations; it is also applied to a time series change point problem previously discussed by Gordon & Smith (1990). For the first example t