The estimation of remaining useful life (RUL) of a faulty component is at the center of system prognostics and health management. It gives operators a potent tool in decision making by quantifying how much time is left until functionality is lost. This is especially true for aerospace systems, where unanticipated subsystem downtime may lead to catastrophic failures. RUL prediction needs to contend with multiple sources of error like modeling inconsistencies, system noise and degraded sensor fidelity. Bayesian theory of uncertainty management provides a way to contain these problems by integrating out the nuisance variables. We use the Relevance Vector Machine (RVM), for model development. RVM is a Bayesian treatment of the well known Support Vector Machine (SVM), a kernel-based regression/classification technique. This model is next used in a Particle Filter (PF) framework. Statistical estimates of the noise in the system and anticipated operational conditions are processed to provide estimates of RUL in the form of a probability density function (PDF). Validation of this approach on experimental data collected from Li-ion batteries is presented.