The problem of missing or lost data is of great importance. In this article we deal with this problem by a new method and technique. This method and technique are concerned with estimating the lost data, using a new procedure based on the conditional expectation. It is applied in four cases: Noisy Markov random fields, noisy autoregressive processes, estimation in hidden Markov chains and simple Gaussian mixture. In each case we derived new formulae concerning this case. The mean and the variance of the Gaussian white noise process (process filtering) are obtained. An illustrative example of two sequences of earthquakes in two neighbor towns during Tsunami catastrophes is given using simulation.
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