Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [beta-binomial-distribution]

The beta-binomial is a discrete distribution on 0, 1, ..., n where the probability of success in a binomial distribution (p) is itself drawn from a beta distribution.

The beta-binomial disribution is a discrete distribution on 0, 1, ..., n.

It arises as a mixture distribution, where the probability of success in a binomial distribution (p) is itself drawn from a beta distribution. Because of this it is sometimes used as a model for heterogeneous mixtures of binomials or more generally for situations where the variance of a discrete distribution on 0, 1, ..., n has a larger variance than the binomial.

It also commonly occurs in Bayesian applications.

Reference: Wikipedia - Beta-binomial distribution

188 questions
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Properly interpret the alpha / beta parameters in the Beta Distribution

For quite a while I believed that the proper interpretation of a Beta distribution with $\alpha$ and $\beta$ is: "what is the most likely $P$ given $\alpha -1 $ success (heads), and $\beta -1 $ of failures (tails)", which also made sense when…
Yehoshaphat Schellekens
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Which distributions on [0,1] other than the beta distribution form nice compounds with the binomial distribution?

For which distributions x, other than beta, is the x-binomial distribution nice? The beta and binomial distributions are famously conjugate but I am curious if other non-conjugate distributions will give comparably simple compound pmfs. By nice I…
gam
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Use Bayesian hierarchical model to predict new data points

I have a data set $(n_i,y_i),i=0,...,10$. I modeled it as a Bayesian hierarchical beta-binomial model. $y_i∼Binomial(n_i,p_i)$ and $p_i∼Beta(\alpha,\beta)$. I have used MCMC to estimate $\alpha$ and $\beta$ (use the median as the estimated…
user22062
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help computing the beta likelihood when we only observe the number of successes and failures (not the latent probability of success)

Imagine we have a biased coin that generates heads with unknown probability $\theta$ where $\theta$ is drawn from a beta distribution with known parameters $(\alpha, \beta)$. Next imagine that we flip the coin some number of times and we get $m$…
ted
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