Most of modern Bayesian statistics is done using Markovian methods (see the next section), but for some problems those methods can be too slow. Variational methods are an alternative that could be a better choice for large datasets (think big data) and/or for posteriors that are too expensive to compute.
The general idea of variational methods is to approximate the posterior distribution with a simpler distribution, in a similar fashion to the Laplace method but in a more elaborate way. We can find this simpler distribution by solving an optimization problem consisting of finding the closest possible distribution to the posterior under some way of measuring closeness. A common way of measuring closeness between distributions ...
