Bayesian Updates and Conjugate Priors

Learn how to update Bayesian models with new information and understand the critical role of conjugate priors in maintaining computational efficiency. Explore the fundamental concept that as posteriors become priors for subsequent updates, keeping the likelihood times prior within the same distribution family simplifies calculations. Discover why conjugate priors are essential when the likelihood and prior distributions become "conjugate," ensuring mathematical tractability. Examine the relationship between binomial and beta distributions as a key example of conjugate pairs, and study the informal definition of conjugate priors along with other important conjugate relationships. Master the process of updating beta distributions and apply these concepts through a practical code demonstration involving coin flip experiments that illustrates how Bayesian updating works in real scenarios.