Bayes' Theorem is a mathematical formula for determining conditional probability. Conditional probability is the likelihood of an outcome occurring, based on a previous outcome having occurred in similar circumstances. Bayes' theorem provides a way to revise existing predictions or theories (update probabilities) given new or additional evidence. In finance, Bayes' Theorem can be used to rate the risk of lending money to potential borrowers. The theorem is also called Bayes' Rule or Bayes' Law and is the foundation of the field of Bayesian statistics.The application of Bayesian statistics has become increasingly important in modern data analysis because it allows for more accurate predictions by taking into account new information as it becomes available. In business and finance, for example, using Bayesian methods can help identify which customers are most likely to default on loans so that lenders can focus their efforts on those borrowers who are most at risk. Additionally, in medical research, scientists use bayesian inference to update their understanding of how diseases progress over time as they gather new data from patients.
