A prior distribution is a key concept in Bayesian statistics that represents what is known about a parameter before observing any data. It reflects the beliefs or information about the parameter based on previous studies, expert opinions, or theoretical considerations. This distribution is essential for incorporating prior knowledge into the analysis, allowing statisticians to update their beliefs as new data becomes available.
When new data is collected, the prior distribution is combined with the likelihood of the observed data to produce a posterior distribution. This updated distribution provides a more accurate estimate of the parameter, taking into account both prior knowledge and the new evidence. The process of updating beliefs in this way is a fundamental aspect of Bayesian inference.