The mini mental state examination (MMSE) is a common tool for measuring cognitive decline in Alzhiemer's Disease (AD) subjects. Subjects are usually observed for a specified period of time or until death to determine the trajectory of the decline which for the most part appears to be linear. However, it may be noted that the decline may not be modeled by a single linear model over a specified period of time. There may be a point called a change point where the rate or gradient of the decline may change depending on the length of time of observation. A Bayesian approach is used to model the trajectory and determine an appropriate posterior estimate of the change point as well as the predicted model of decline before and after the change point. Estimates of the appropriate parameters as well as their posterior credible regions or regions of interest are established. Coherent prior to posterior analysis using mainly non-informative priors for the parameters of interest is provided. This approach is applied to an existing AD database. © 2009 IMACS.