3 ms·
> A beta prior is equivalent to assigning “pretend votes” to each new item. Instead of starting out with 0 upvotes and 0 downvotes, we start out with a upvotes
by igonvalue 11y ago
> A beta prior is equivalent to assigning “pretend votes” to each new item. Instead of starting out with 0 upvotes and 0 downvotes, we start out with a upvotes and b downvotes. If we expect that most items are bad, we could start with 3 upvotes and 10 downvotes. After getting u real upvotes, and d real downvotes the posterior distribution is Beta(a+u, b+d).
Fascinating. Does this follow as a straightforward consequence of how the beta distribution is defined? Otherwise, is there a proof that someone could point me toward?
> The popularity of an item has a Beta(a,b) prior
Is there an optimal choice of a, b given, say, a specific utility function?
- wuch 11y agoBeta is conjugate prior of binomial distribution. That means is you start with prior beta, and likelihood has binomial distribution, then posterior obtained using Bayes theorem also will have beta distribution (with different paramters). If you look up definition of beta distribution and then write down formula for posterior it should be quite clear that result is also beta distribution - modulo normalizing constant which may be a little more tricky to determine.
- dragandj 11y agoThis is the Hello World of bayesian data analysis. A discussion and examples could be found in literally every bayesian textbook.