Most data assimilation methods can be derived from Bayes’ theorem but crucial differences exist in the algorithms:

• Variational (Var) techniques aim to find the maximum a posteriori estimate of the state assuming Gaussian error statistics (i.e. they can be fully quantified by their mean and covariances) and near-linear models. Var often makes use of a climatological estimate of the prior error covariances and considers a time window of observations.
• Ensemble data assimilation techniques, such as EnKF, assimilate observations sequentially in time and use an ensemble of model states to evolve the prior uncertainty. The EnKF is similar to Var in that it still assumes that the error statistics are Gaussian.
• Lastly there are techniques such as the particle filter which avoid making any assumptions about the error distributions and try to provide a complete representation of the posterior, whether that be Gaussian, skewed or multi-modal.

The best method to use depends on the intended application, as the validity of assumptions and the data available differ substantially between e.g. monitoring changes to the land surface, numerical weather prediction and forecasting the ocean ecosystem.