As human beings we have to make decisions on a daily basis. As our knowledge or evidence about a certain phenomenon increases, we update our outlook as a result of the new knowledge.
In a world where we encounter lots of probabilities, it is important to use the same thinking as opposed to confining ourselves to frequentist statistics that does not necessarily take new evidence into consideration.
Many professionals, such as medical doctors and judges in court, are expected to make important decisions based on statistical information. Often, Bayesian inferences are required, for example when a radiologist has to judge and communicate the statistical meaning of a positive mammography screening. Many empirical studies have documented faulty inferences and even cognitive illusions among professionals of various disciplines.
In the medical context, the consequences are particularly severe because many patients are mistakenly found diseased, which can entirely change their lives.
Similarly, insufficient knowledge of statistics in general and incorrect Bayesian reasoning in particular can result in false convictions or acquittals made by juries in court, for example when they have to evaluate evidence based on a fragmentary DNA sample. These faults bear the risk of destroying innocent people's lives.