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For linear and Gaussian systems, fault detection over a batch of data is well-studied, and analytical solutions exist in a stochastic framework. The parity space approach handles additive faults and can be shown to be equivalent to estimating the state trajectory and then removing its influence on the output sequence. Multiplicative faults in linear systems can be handled using parameter estimation methods, such as the EM-algorithm in combination with the Kalman smoother. For nonlinear and non-Gaussian systems, we propose to estimate the state trajectory and the faults over the data batch using a particle smoother and the EM-algorithm. The result is a generic fault detection and isolation scheme that applies to arbitrary nonlinear and non-Gaussian systems, where the faults are monitored over a sliding window.