Beta distribution is conjugate to binomial likelihood
Beta-binomial distribution
Beta distribution is conjugate to binomial likelihood
The beta distribution serves as a conjugate prior for the binomial distribution in Bayesian statistics. This conjugacy simplifies the process of updating beliefs with new data, as the posterior distribution remains within the same family of distributions.
Example
Suppose we have 10 coin flips with an unknown probability of heads. If we start with a beta distribution prior for the probability of heads, after observing the outcomes, our posterior distribution will also be a beta distribution, reflecting the updated beliefs about the probability of heads.
Remember this
Understanding conjugate priors like the beta distribution is crucial for efficient Bayesian inference, as it allows for straightforward updating of probability distributions with new evidence.
Text adapted from Wikipedia, licensed under CC BY-SA 4.0.
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