Variational inference applied to a univariate Gaussian

Implementation and more is provided in the notebook "Variational_inference_UG.ipynb"

Adapted from the two books: Pattern Recognition and Machine Learning Christopher M. Bishop and A Probabilistic Perspective Murphy 2012.

Given a data set:

which are i.i.d and drawn from a 1d Gaussian which likelihood function is given by:

Where the conjugate prior distributions for is given by:

With the mean field method we factorize the approximate distribution such that it is given by:

The following video sequence was generated with 15 data points and the following parameters:

And the following shows the exact posterior with the approximate (20 data points):

Where the exact posterior is given by:

Murphy, K. P. (2007). Conjugate Bayesian analysis of the Gaussian distribution. def, 1(2σ2), 16.