BAYESIAN METHODS

Bayesian methods provide a natural way to structure data and knowledge. The approach is often difficult to use and requires considerable time and effort. In addition, the methods require the user to apply subjective judgment and assumptions to the analysis. This makes them difficult to apply without a strong incentive. This article aims to provide a basic introduction to the use of Bayesian methods and discuss their strengths and weaknesses.
Bayesian methods were originally developed by De Finetti, Savage, and Jaynes. While this method was enthusiastically embraced by the nineteenth century, its popularity faded over the decades. In the twentieth century, it fell out of favor, largely due to a lack of understanding of how to handle prior probabilities. As a result, a new theory was developed, now known as frequentist statistics. Nevertheless, Bayesian thinking survived thanks to pioneers such as Bruno de Finetti in Italy and Harold Jeffreys in England.
Bayesian methods have many applications, and many statistics practitioners advocate their use. Moreover, the approach is philosophically consistent. There are logical reasons to use Bayesian methods rather than frequentist methods. For example, prior probabilities are subjective, a problem with frequentist methods. Furthermore, they require the user to take into account their own prior knowledge. Consequently, many statisticians see this as a fundamental weakness of frequentist methods.
Bayesian methods can be particularly useful in rare disease settings. In particular, the INHIBIT trial design is used to investigate the development of inhibitors among previously untreated patients. Since inhibitors occur in fewer patients than in previously treated patients, this study design may lead to zero incidences for important outcomes. As a result, Bayesian methods provide a natural solution to this problem.