This dissertation consists of three essays in Bayesian time-series analysis. In the first essay, I propose a simple and convenient method for analyzing spatio-temporal data. To account for spatial variability in the data, the mean funcion at each time is written as a loaclly-weighted mixture of linear regressions.
Temporal variation is modeled by allowing the regression coefficients to change through time.
The model is cast in a Gaussian state-space framework, allowing us to explore temporal factors such as trends, seasonality, and autoregressive components. This allows quick implementation of the model, and provides full probabilistic inference for the parameters, interpolations, and forecasts. The method can be used to conduct posterior inference in a broad class of dynamic models. The key idea is to construct an approximate state-space model based on mixtures of nomals. This approximation is then used to define the proposal distribution in an efficient Metropolis-Hastings MCMC algorithm, which provides samples from the posterior distribution.