Prior Distributions
In Bayesian statistics, a prior distribution represents our beliefs about a parameter before observing any data. It quantifies what we know or assume about the parameter based on previous knowledge, experience, or theoretical considerations. This distribution is crucial because it influences the results of the analysis when combined with new data.
When new data is collected, the prior distribution is updated to form a posterior distribution using Bayes' theorem. This process allows statisticians to refine their beliefs and make more informed predictions. The choice of prior can significantly affect the outcome, making it essential to select it carefully based on the context of the problem.