*Introductory Chapter: Development of Bayesian Inference DOI: http://dx.doi.org/10.5772/intechopen.108011*

variables in a high-dimensional regression model, which have received considerable attention and extended to various models such as generalized linear models and linear mixed models. In particular, to reduce the computational cost, various variational Bayesian methods have been developed for various models in recent years. For example, see linear mixed models [16] and reference therein. However, there are a lot of unsolved problems. For example, for a complicated model, how to find the optimal variational densities for approximating complicated posterior distributions? How to extend/break the assumption of mean field that is a basic assumption in variational analysis? How to utilize other divergence criteria rather than Kullback–Leibler divergence to develop variational Bayesian theories?
