  This paper focuses on utilizing two different Bayesian methods to deal with a
variety of toy problems which occur in data analysis. In particular we
implement the Variational Bayesian and Nested Sampling methods to tackle the
problems of polynomial selection and Gaussian Mixture Models, comparing the
algorithms in terms of processing speed and accuracy. In the problems tackled
here it is the Variational Bayesian algorithms which are the faster though both
results give similar results.
