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What is a beta prior?
In the literature you’ll see that the beta distribution is called a conjugate prior for the binomial distribution. This means that if the likelihood function is binomial, then a beta prior gives a beta posterior. In fact, the beta distribution is a conjugate prior for the Bernoulli and geometric distributions as well.
What is the beta distribution used to model?
The beta distribution is used to model continuous random variables whose range is between 0 and 1. For example, in Bayesian analyses, the beta distribution is often used as a prior distribution of the parameter p (which is bounded between 0 and 1) of the binomial distribution (see, e.g., Novick and Jackson, 1974).
Do you know the posterior is a beta distribution?
If we choose to use the beta distribution as a prior, during the modeling phase, we already know the posterior will also be a beta distribution.
How is the intuition for the beta distribution?
The intuition for the beta distribution comes into play when we look at it from the lens of the binomial distribution. The difference between the binomial and the beta is that the former models the number of successes (x), while the latter models the probability (p) of success.
How is the beta distribution used in Bayesian inference?
The computation in Bayesian Inference can be very heavy or sometimes even intractable. But if we could use the closed-form formula with the conjugate prior, the computation becomes a piece of cake. In our date acceptance/rejection example, the beta distribution is a conjugate prior to the binomial likelihood.
When is a beta posterior a conjugate prior?
In the literature you’ll see that the beta distribution is called aconjugate priorfor thebinomial distribution. This means that if the likelihood function is binomial, then a betaprior gives a beta posterior. In fact, the beta distribution is a conjugate prior for theBernoulli and geometric distributions as well.