In this chapter, we undertook a whirlwind tour of one of the hottest trends in statistics and data analysis in the past few years—the Bayesian approach to statistical inference. We covered a lot of ground here.

We examined what the Bayesian approach to statistics entails and discussed the various reasons why the Bayesian view is a compelling one, such as the fact that it values facts over belief. We explained the key statistical distributions and showed how we can use the various statistical packages to generate and plot them in matplotlib.

We tackled a rather difficult topic without too much oversimplification and demonstrated how we can use the PyMC package and Monte Carlo simulation methods to showcase the power of Bayesian statistics to formulate models, perform trend analysis, and make inferences on a real-world dataset (Facebook user posts). The concept of maximum likelihood estimation was also introduced and explained with several examples. It is a popular method for estimating distribution parameters and fitting a probability distribution to a given dataset.

In the next chapter, we will discuss how we can solve real-life data case studies using pandas.