Condition based maintenance of machinery is being much talked about in the engineering sector of defense and commercial industry. A lot of expenditure is generally incurred on condition monitoring of machinery to avoid unexpected downtimes and failures vis-à-vis optimizing machinery operation. The concept is ever evolving due to technological advancements as well as with the emergence of unique nature of defects in complex systems. The features of machinery health extracted through modern condition monitoring technologies helps in diagnostics of current health; however, utilizing the current data for prediction of future machinery state i.e Prognostics is a challenging task. Prognostic is one of the key elements of modern maintenance philosophies. Effective prognostic, from the machinery data, leads towards operational reliability, reduced machinery downtime, cost savings, secondary/catastrophic failures etc. Machinery health prognosis follows a sequential methodology inclusive of various processes ranging from data acquisition till remaining useful life estimation. Every step depicts distinct statistical features, which are helpful in estimating present and future health state of a machine. Various methodologies have been adopted by the researchers in an effort to precisely forecast/predict machinery health. Research in this area, where stochastic models have been applied, revealed encouraging results. In this thesis, we have presented three nonlinear stochastic models with their application on bearing health prognosis. These include Markov Switching Auto Regressive Model with Time Varying Regime Probabilities, Threshold Auto Regressive Model and Structural Break Point Classifier Model. The results showed that the applied models can be effectively utilized for data driven machinery health prognosis.