Bayesian Statistics is an approach to statistics based on the work of the 18th century statistician and philosopher Thomas Bayes, and it is characterized by a rigorous mathematical attempt to quantify uncertainty. The likelihood of uncertain events is unknowable, by definition, but Bayes’s Theorem provides equations for the statistical inference of their probability based on prior information about an event - which can be updated based on the results of new data.

While its origins lie hundreds of years in the past, Bayesian statistical approaches have become increasingly important in recent decades. The calculations at the heart of Bayesian statistics require intensive numerical integrations to solve, which were often infeasible before low-cost computing power became more widely accessible. But today, statisticians can evaluate integrals by running hundreds of thousands of simulation iterations with Markov chain Monte Carlo methods on an ordinary laptop computer.

This new accessibility of computational power to quantify uncertainty has enabled Bayesian statistics to showcase its strength: making predictions. This capability is critical to many data science applications, and especially to the training of machine learning algorithms to create predictive analytics that assist with real-world decision-making problems. As with other areas of data science, statisticians often rely on R programming and Python programming skills to solve Bayesian equations.