Understanding Bayes' Theorem

Bayes' Theorem is a statistical principle developed in the 18th century that has become integral to modern probability and statistics. It shifts the focus from asking how likely a set of data is under a given hypothesis to determining how likely that hypothesis is given new data. This distinction is crucial for scientists, as they often want to validate their theories based on empirical evidence rather than merely assessing the probability of observables. The theorem uses what is called prior probabilities—existing beliefs or information—to derive new probabilities about hypotheses, thus providing a framework for updating beliefs based on new evidence.