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Time series segmentation is a dynamic sphere of research that has attracted attention in diverse topics. The aim of this thesis is to segment time series data using a Bayesian approach and develop methods to segment multiple parallel time series data. This thesis used a novel methodology called the Bayesian change-point segmented ARMA model, which estimates the change-point locations by segmenting a time series using an ARMA model. It also uses a highly efficient technique (Generalized Gibbs Sampler) to generate samples from a posterior distribution. Three alternative generalizations of the Bayesian change-point segmented ARMA model were developed to segment multiple parallel time series data.

Time series segmentation aims to identify segment boundary points in a time series, and to determine the dynamical properties corresponding to each segment. To segment time series data, this article presents a Bayesian change-point model in which the data within segments follows an autoregressive moving average (ARMA) model. A prior distribution is defined for the number of change-points, their positions, segment means and error terms. To quantify uncertainty about the location of change-points, the resulting posterior probability distributions are sampled using the Generalized Gibbs sampler Markov chain Monte Carlo technique. This methodology is illustrated by applying it to simulated data and to real data known as the well-log time series data. This well-log data records the measurements of nuclear magnetic response of underground rocks during the drilling of a well. Our approach has high sensitivity, and detects a larger number of change-points than have been identified by comparable methods in the existing literature.

Sample size determination is a prerequisite for statistical surveys. A comprehensive overview of the Bayesian approach for computation of the sample size, and a comparison with classical approaches, is presented. Two surveys are taken as example to illustrate the accuracy and efficiency of each approach, and to make recommendations about which method is preferred. The Bayesian approach of sample size determination may require fewer subjects if proper prior information is available.