Variational Bayesian Methods - A Basic Example

A Basic Example

Consider a simple non-hierarchical Bayesian model consisting of a set of i.i.d. observations from a Gaussian distribution, with unknown mean and variance. In the following, we work through this model in great detail to illustrate the workings of the variational Bayes method.

For mathematical convenience, in the following example we work in terms of the precision — i.e. the reciprocal of the variance — rather than the variance itself. (From a theoretical standpoint, precision and variance are equivalent since there is a one-to-one correspondence between the two.)